BBC Russian

Preprint ARTICLE | doi:10.20944/preprints202409.1972.v1

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; Robin inequality; Sum-of-divisors function; Prime numbers; Riemann zeta function

Online: 25 September 2024 (12:09:06 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.1852.v1

Symmetric Reverse $n$-Derivations on Ideals of Semiprime Rings

Shakir Ali, Ali Y. Hummdi, Naira N. Rafiquee, Vaishali Varshney, KokBin Wong

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Semiprime ring; ideal; symmetric $n$-derivation; symmetric reverse $n$-derivation; derivation; trace of symmetric map

Online: 24 September 2024 (11:59:35 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.1294.v1

Huan Xiao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann zeta function; Riemann hypothesis

Online: 18 September 2024 (11:12:31 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.1002.v1

Dynamics and Forms of Products of Twin, Cousin and Sexy Primes

Ahmet F. Gocgen, Emin M. Buyukyayla

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: number theory; cousin primes; product of cousin primes; prime products

Online: 12 September 2024 (14:09:37 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1161.v4

A Note on Oppermann's Conjecture

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime gaps; prime numbers; square root; inequality

Online: 12 September 2024 (10:56:11 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.0541.v2

The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9

seyed kazem mousavi

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime numbers; Riemann's hypothesis; three numbers 3; 6; 9

Online: 11 September 2024 (15:29:13 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.0541.v1

The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9

seyed kazem mousavi

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime numbers; Riemann's hypothesis; three numbers 3; 6; 9

Online: 6 September 2024 (12:07:54 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1416.v2

On the Natural Numbers that cannot be Expressed as a Sum of Two Primes

Peter Szabó

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: circulant matrix; prime number; the Goldbach conjecture; the ternary Goldbach conjecture

Online: 5 September 2024 (10:42:32 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1439.v2

Apocalyptic Proof of the Riemann Hypothesis with the Generating Function for Prime Numbers

Mojtaba Jalali Koutanaei

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Zeta Function; Number Theory; Riemann's Hypothesis

Online: 4 September 2024 (04:42:56 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.0181.v1

On Nilpotent Elements and Armendariz Modules

Nazeer Ansari, Kholood Alnefaie, Shakir Ali, Adnan Abbasi, Kh. Herachandra Singh

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Nilpotent element; Armendariz module; Armendariz ring; nil-Armendariz module

Online: 3 September 2024 (07:55:50 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.0039.v1

On Some Special Cases of K ¨othe’s Conjecture

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: K$\ddot{o}$the Conjecture; Rings; Ideals; Nil Ideal; Jacobson Radical; Nilpotent; Noetherian Rings; Artinian Rings; Two-Sided Ideals; K$\ddot{o}$the Subsets; Commutative Rings; Matrix Rings; Polynomial Rings; Algebra; Tensor Product; Modules; Field Extension

Online: 2 September 2024 (13:18:01 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.0090.v1

Representations of the G-drazin Inverse for Certain Anti-triangular Matrices

Huanyin Chen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Drazin inverse; g-Drazin inverse; anti-triangular matrix; quadratic equation; Banach algebra

Online: 2 September 2024 (10:52:12 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202409.0063.v1

Ternary Associativity and Ternary Lie Algebra at Cube Root of Unity

Viktor Abramov

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Lie algebra; ternary associativity of the first and second kind; ternary algebra; ternary commutator; ternary Lie algebra at cube root of unity; general affine group

Online: 2 September 2024 (09:47:15 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1161.v3

A Note on Oppermann's Conjecture

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime gaps; prime numbers; Chebyshev function; primorial numbers

Online: 23 August 2024 (09:45:01 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.0451.v2

On Proving Ramanujan’s Inequality Using a Sharper Bound for the Prime Counting Function π(x)

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Ramanujan; Prime counting function; Chebyshev Theta function; Mathematica; Primes

Online: 22 August 2024 (02:51:25 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1439.v1

Apocalyptic Proof of the Riemann Hypothesis with the Generating Function for Prime Numbers

Mojtaba Jalali Koutanaei

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Zeta Function; Number Theory; Riemann's Hypothesis

Online: 21 August 2024 (04:31:23 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1161.v2

A Note on Oppermann's Conjecture

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime gaps; prime numbers; Euler-Maclaurin formula; harmonic numbers

Online: 21 August 2024 (04:30:04 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0759.v3

On proving an Inequality of Ramanujan using Explicit Order Estimates for the Mertens Function

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Zeta Function; Mertens Function; Chebyshev Function; arithmetic function; error estimates; Perron’ s Formula; M¨; obius Inversion Formula; Dirichlet Partial Summation Formula

Online: 21 August 2024 (00:08:05 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1416.v1

On the Natural Numbers that cannot be Expressed as a Sum of Two Primes

Peter Szabó

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: circulant matrix; prime number; the Goldbach conjecture; the ternary Goldbach conjecture

Online: 20 August 2024 (12:03:53 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1276.v6

Inequalities involving Higher Degree Polynomial Functions in $\pi(x)$

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Function; Second Chebyshev Function; prime counting function; Prime Number Theorem; Error Estimates; Higher-Degree Polynomials; weighted sums; logarithmic weighted sums

Online: 20 August 2024 (08:42:50 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202002.0379.v14

A Note on Riemann Hypothesis

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; prime numbers; Riemann zeta function; Chebyshev function

Online: 19 August 2024 (14:35:05 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202109.0480.v8

A Note on Fermat’s Last Theorem

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Fermat’ s equation; prime numbers; coprime integers

Online: 19 August 2024 (11:18:42 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1301.v1

Square-Difference Factor Absorbing Primary Ideals of Commutative Rings

Hani A. Khashan, Ece Yetkin Çelikel, Unsal Tekir

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime ideal; primary ideal; square-difference factor absorbing ideal; square-difference factor absorbing primary ideal

Online: 19 August 2024 (09:51:37 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1161.v1

A Note on Oppermann's Conjecture

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime gaps; prime numbers; Euler-Maclaurin formula; harmonic numbers

Online: 16 August 2024 (03:00:22 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.1127.v1

A Recurrent Proof of the Fundamental Theorem of Algebra

Vincenzo Manca

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Fundamental Theorem of Algebra; Recurrent Equation; Polynomial Coefficient Function; Complex Hyperspace

Online: 15 August 2024 (15:19:41 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202108.0146.v34

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof of; completed zeta function; Hadamard product

Online: 15 August 2024 (14:31:12 CEST)

Show abstract| Download PDF| Supplementary Files| Share

Preprint ARTICLE | doi:10.20944/preprints202002.0379.v13

A Note on Riemann Hypothesis

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; prime numbers; Riemann zeta function; Chebyshev function

Online: 14 August 2024 (09:22:47 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202109.0480.v7

A Note on Fermat’s Last Theorem

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Fermat's Equation; Prime Numbers; Coprime Numbers

Online: 13 August 2024 (07:51:25 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.0348.v2

Robin’s Criterion on Superabundant Numbers

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; Robin's criterion; superabundant numbers; prime numbers

Online: 13 August 2024 (05:32:52 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.0451.v1

On Proving Ramanujan’s Inequality using a Sharper Bound for the Prime Counting Function π(x)

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ramanujan; prime counting function; chebyshev theta function; mathematica; primes

Online: 8 August 2024 (11:53:54 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.0348.v1

Robin’s Criterion on Superabundant Numbers

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; Robin's criterion; superabundant numbers; prime numbers

Online: 6 August 2024 (06:56:30 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202408.0216.v1

Generalized core-EP inverse for triangular operator matrices

Huanyin Chen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: core inverse; core-EP inverse; generalized core-EP inverse; triangular matrix; Block operator matrix; Banach algebra

Online: 4 August 2024 (23:35:06 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.2549.v1

On Non Commutative Multirings with Involutions

Kaique Ribeiro Santos, Hugo Luiz Luiz Mariano, Kaique Matias de Andrade Roberto

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: multirings; involutions; abstract real algebra

Online: 31 July 2024 (14:11:40 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.2425.v1

An In-depth Evaluation of Educational Burst Games - in Relation to Learner Proficiency

Ashish Amresh, Vipin Verma, Michelle Zandieh

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ; game-based learning; assessment; design; proficiency

Online: 30 July 2024 (09:08:07 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.2314.v1

Development of a Simple Prime Number Determination Method by excluding Composite Numbers on 6n±1

Haruhiro Shiraishi, Hajime Shiraishi, Yukiya Taniguchi

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Prime numbers; Composite numbers; 6n±; 1

Online: 30 July 2024 (00:07:38 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0759.v2

On proving an Inequality of Ramanujan using Explicit Order Estimates for the Mertens Function

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Zeta Function; Mertens Function; Chebyshev Function; arithmetic function; error estimates; Perron’ s Formula; M¨; obius Inversion Formula; Dirichlet Partial Summation Formula

Online: 26 July 2024 (16:51:08 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202309.0723.v2

On Some Specific Order Estimates for the Mertens Function and Its Relation to the Non-trivial Zeros of $\zeta(s)$

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: arithmetic function; Mo¨bius function; Riemann Zeta function; Mertens function; Redheffer Matrix; Riemann Hypothesis; Roesler Matrix; spectral radius; Mertens Hypothesis

Online: 26 July 2024 (13:01:23 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0961.v5

$2^m - 1$ as the Integer Formulation to Govern the Dynamics of Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz; 3n+1

Online: 25 July 2024 (14:59:59 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1276.v5

Inequalities involving Higher Degree Polynomial Functions in $\pi(x)$

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Function; Second Chebyshev Function; Prime Counting Function; Prime Number Theorem; Error Estimates; Higher-Degree Polynomials; Weighted Sums; Logarithmic Weighted Sums

Online: 25 July 2024 (12:05:09 CEST)

Show abstract| Download PDF| Supplementary Files| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1276.v4

Inequalities involving Higher Degree Polynomial Functions in $\pi(x)$

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Function; Second Chebyshev Function; Prime Counting Function; Prime Number Theorem; Error Estimates; Higher-Degree Polynomials; Weighted Sums; Logarithmic Weighted Sums

Online: 24 July 2024 (07:32:58 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0961.v4

$2^m - 1$ as the Integer Formulation to Govern the Dynamics of Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz; 3n+1

Online: 23 July 2024 (16:06:28 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202109.0480.v6

A Note on Fermat’s Last Theorem

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Fermat's Equation; Prime Numbers; Coprime Numbers

Online: 23 July 2024 (13:53:56 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1276.v3

Inequalities involving Higher Degree Polynomial Functions in $\pi(x)$

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Function; Second Chebyshev Function; Prime Counting Function; Prime Number Theorem; Error Estimates; Higher-Degree Polynomials; Weighted Sums; Logarithmic Weighted Sums

Online: 23 July 2024 (11:26:51 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202108.0146.v33

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof of; completed zeta function; Hadamard product

Online: 23 July 2024 (07:35:43 CEST)

Show abstract| Download PDF| Supplementary Files| Share

Preprint ARTICLE | doi:10.20944/preprints202109.0480.v5

A Note on Fermat’s Last Theorem

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Fermat's Equation; Prime Numbers; Coprime Numbers

Online: 23 July 2024 (07:33:25 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0961.v3

$2^m - 1$ as the Integer Formulation to Govern the Dynamics of Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz; 3n+1

Online: 22 July 2024 (11:55:52 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1276.v2

Inequalities involving Higher Degree Polynomial Functions in π(x)

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Function; Second Chebyshev Function; Prime Counting Function; Prime Number Theorem; Error Estimates; Higher-Degree Polynomials; Weighted Sums; Logarithmic Weighted Sums

Online: 22 July 2024 (05:19:42 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1648.v1

Recursive Formula for Sum of Powers of Natural Numbers and Its Generalization to Arithmetic Progression

Ahmad Daffa I. F. Askari

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sum of powers; arithmetic progression; bernoulli numbers

Online: 22 July 2024 (04:58:09 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0961.v2

$2^m - 1$ as the Integer Formulation to Govern the Dynamics of Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz; 3n+1

Online: 18 July 2024 (14:33:11 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1312.v1

Calculation of the Number of Transactions for Collatz Conjecture

Ahmet F. Gocgen, Emin M. Buyukyayla

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: collatz conjecture; beal’ s conjecture; composite numbers; recursive structure; number of transactions

Online: 16 July 2024 (09:24:14 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1276.v1

Studying some Inequalities involving Polynomial Functions in π(x)

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Function; Second Chebyshev Function; Prime Counting Function; Prime Number Theorem; Error Estimates; Polynomials

Online: 16 July 2024 (08:04:33 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.1030.v1

Tangential and Anisotropic Bases in Quadratic Spaces

Alexander Leones, Pedro Hurtado, John Moreno, Adolfo Pimienta

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: quadratic space; isotropic vector; orthogonal basis; tangential basis; anisotropic basis

Online: 15 July 2024 (10:51:17 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0961.v1

$2^m - 1$ as the Integer Formulation to Govern the Dynamics of Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz, 3n+1

Online: 11 July 2024 (12:28:15 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202407.0759.v1

On proving an Inequality of Ramanujan using Explicit Order Estimates of the Mertens Function

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Zeta Function; Mertens Function; Chebyshev Function; arithmetic function; error estimates; Perron’ s Formula; M¨; obius Inversion Formula; Dirichlet Partial Summation Formula

Online: 9 July 2024 (16:22:12 CEST)

Show abstract| Download PDF| Share

Preprint COMMUNICATION | doi:10.20944/preprints202407.0103.v1

Cauchy-Riemann Equations for Treons

Alejandro Jesús Bermejo Valdés

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Cauchy-Riemann equations; treonic number; treons; algebra B; Bermejo's algebra

Online: 1 July 2024 (13:26:58 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.1867.v1

Generalized weighted group inverse in Banach algebras with proper involution

Huanyin Chen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: weighted generalized Drazin inverse; weighted group inverse; weak group inverse; complex matrix; Banach algebra.

Online: 27 June 2024 (08:10:56 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202002.0379.v12

Note for the Riemann Hypothesis

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; Prime numbers; Riemann zeta function; Chebyshev function

Online: 25 June 2024 (10:26:09 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202002.0379.v11

Note for the Riemann Hypothesis

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; Prime numbers; Riemann zeta function; Chebyshev function

Online: 24 June 2024 (08:58:02 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.0256.v2

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 24 June 2024 (08:08:06 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202002.0379.v10

Note for the Riemann Hypothesis

Frank Vega

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann hypothesis; Prime numbers; Riemann zeta function; Chebyshev function

Online: 21 June 2024 (10:43:53 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.1385.v1

Analysis of Complex Entities in Algebra B

Alejandro Jesús Bermejo Valdés

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: isomorphism; treonic number; algebra B; Euler identity; hyperbolic

Online: 20 June 2024 (08:30:58 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.1296.v1

A proof of the infinitude of prime numbers

Md. Shouvik Iqbal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Prime Numbers, Infinitude of Primes, Euclid's theorem, Proof of Euclid's theorem, Proof of Infinitude of Primes, Set Theory, Proof by Contradiction.

Online: 19 June 2024 (11:17:14 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.1246.v1

Generalized Right Core Inverse in *-Banach Algebras

Huanyin Chen, Marjan Sheibani

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: core inverse; right core inverse; core-EP inverse; right core-EP inverse; generalized right core inverse; polar-like property; *-Banach algebra

Online: 18 June 2024 (14:14:02 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.1110.v1

First Exploration of a Novel Generalization of Lie and Malcev Algebras Leading to the Emergence of Complex Structures

Alejandro Jesús Bermejo Valdés

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: algebra B; Lie algebra; Malcev algebra; non-associative algebra

Online: 17 June 2024 (07:59:04 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202108.0146.v32

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof of; completed zeta function; Hadamard product; transfinite induction

Online: 14 June 2024 (14:56:25 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.0554.v1

A Rational Approximation of the Two-Term Machin-Like Formula for π

Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: constant pi; iteration; nested radicals; rational approximation

Online: 10 June 2024 (09:59:01 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202405.0310.v2

Collatz Conjecture Is Analogous to an Inverse Function of Natural Number

Jishe Feng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: binary string; full binary directed tree; composite function; Collatz conjecture; ultimately periodic sequence

Online: 7 June 2024 (11:04:40 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.0265.v1

A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions

Hany Gerges, Antanas Laurinčikas, Renata Macaitienė

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: dirichlet L-function; epstein zeta-function; hurwitz zeta-function; limit theorem; probability haar measure; weak convergence

Online: 6 June 2024 (02:54:33 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202406.0256.v1

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 5 June 2024 (10:19:24 CEST)

Show abstract| Download PDF| Share

Preprint REVIEW | doi:10.20944/preprints202405.1748.v1

Monogenity and Power Integral Bases: Recent Developments

István Gaál

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: algebraic number fields; index of an element; generators of power integral bases; monogenic number fields; monogenic polynomials; pure fields; trinomials; relative extensions; algorithms

Online: 27 May 2024 (14:05:50 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202108.0146.v31

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 24 May 2024 (08:38:04 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202405.0952.v1

Hyperbolic Primality Test and Catalan–Mersenne Number Conjecture

Youngik Lee

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Catalan-Mersenne conjecture; Mersenne prime; double Mersenne prime

Online: 14 May 2024 (13:53:44 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202405.0707.v1

Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework

Sofiia Ivanko, Peter Farag

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Sophy-Peter Framework, New Number Theory, Modified Collatz Conjecture, Oscillating Theorem, General Zeta Function, Proof of the Riemann Hypothesis

Online: 13 May 2024 (03:09:42 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202405.0510.v1

Using Full Binary Directed Tree Proof the Collatz Conjecture

Jishe Feng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: binary string; full binary directed tree; composite function; Collatz conjecture; ultimately periodic sequence

Online: 8 May 2024 (14:21:59 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202405.0310.v1

Collatz Conjecture Is Analogous to an Inverse Function of Natural Number

Jishe Feng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: binary string; full binary directed tree; composite function; Collatz conjecture; ultimately periodic sequence

Online: 7 May 2024 (03:03:05 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.1750.v1

Abelian Extensions and Crossed Modules of Modified λ-Differential Left-Symmetric Algebras

Fuyang Zhu, Taijie You, Wen Teng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: left-symmetric algebras; modified λ -differential operator; cohomology; deformation; abelian extension; crossed module

Online: 28 April 2024 (03:02:21 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.1559.v1

Jesmanowicz Conjecture and Gaussian Integer Ring

Nianrong Feng, Junyu Cao, Yongzheng Wang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Jesmanowicz conjecture; Diophantine equation; Gaussian integer ring; 4k+1 type prime number

Online: 24 April 2024 (09:32:50 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.1411.v1

Cohomology of Modified Rota-Baxter Pre-lie Algebras and Its Applications

Fuyang Zhu, Taijie You, Wen Teng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Pre-Lie algebras; modified Rota-Baxter operator; cohomology; deformation; abelian extension; pre-Lie 2-algebras

Online: 23 April 2024 (03:17:05 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.0943.v1

Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Binary pattern,Positive integers ,Collatz conjecture

Online: 15 April 2024 (10:55:15 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.0792.v2

Understanding the Boundless Potential of Infinite Numbers in Mathematics

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: infinite series, infinity, infinitesimals

Online: 15 April 2024 (08:46:20 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.0792.v1

Understanding the Boundless Potential of Infinite Numbers in Mathematics

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ; infinity,infinitesimals, infinite series, infinite numbers

Online: 11 April 2024 (11:18:18 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.0778.v1

Collatz Conjecture Proof and General Equation

Kirk O. Hahn

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: collatz conjecture; proof; rules; dendritic pathway

Online: 11 April 2024 (07:07:56 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.0728.v1

Linear Generalized N-derivations on C-algebras*

Vaishali Varshney, Amal S. Alali, Shakir Ali

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Linear derivation; linear n-derivation; generalized linear n-derivation; Lie ideal; Banach algebra; C*-algebra

Online: 10 April 2024 (10:09:03 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202110.0087.v22

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sieve of eratosthenes; goldbach conjecture; polignac conjecture; twin prime conjecture

Online: 4 April 2024 (17:39:40 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202404.0268.v1

Covers of Finitely Generated Acts over Monoids

Xiaoqin Zhang, Tingting Zhao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: cover; coproduct; finitely generated; $\mathcal{X}$-precover

Online: 3 April 2024 (08:28:04 CEST)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202403.1718.v1

Prime Factorization and Diophantine Quintic Equations Insights, Challenges, and New Directions

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: algebraic methods,quintic problem,Diophantine equation ,prime number

Online: 28 March 2024 (09:35:31 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202403.0963.v1

The Generalized Eta Transformation Formulas as the Hecke Modular Relation

Nianliang Wang, Takato kuzumaki, Shigeru Kanemitsu

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: RHB correspondence; transformation formula for Lambert series; Hurwitz zeta-function; Lerch zeta-function; vector space structure

Online: 18 March 2024 (08:12:55 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202403.0664.v1

The Jacobian Conjecture and Idempotent Ideals

Lukasz Matysiak

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: automorphism; idempotent ideal; Jacobian conjecture; polynomial mapping

Online: 12 March 2024 (13:46:14 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202108.0146.v30

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 8 March 2024 (15:56:30 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.1638.v1

Prime Solutions to the Diophantine Equation 2ⁿ = p² +7

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: integers; ; Diophantine Equation; prime number

Online: 28 February 2024 (13:55:57 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.1484.v1

(m, n)-Closed Submodules of Modules over Commutative Rings

Ece Yetkin Celikel, Hani Khashan

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: (m,n)-closed ideals, (m,n)-prime ideals, (m,n)-closed submodules, n-absorbing submodules

Online: 26 February 2024 (15:33:56 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.1143.v1

Finite and Symmetric Euler Sums and Multiple T-Values

Jianqiang Zhao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: (finite) Euler sums; symmetric Euler sums; (finite) multiple T-values; symmetric multiple T-values; alternating multiple T-values

Online: 20 February 2024 (14:34:09 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.1108.v1

Exploring the Connection between Prime Numbers, Trigonometric Functions, and the Riemann Hypothesis through ln(sec(π.nlog(n)))

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime numbers; Riemann Hypothesis; analytic functions; trigonometric functions

Online: 20 February 2024 (08:49:02 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.1003.v1

On Certain Properties of Square-Free Numbers and the Function s(n)

Lukasz Matysiak, Julia Fidler

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: monoid; Riemann hypothesis; square-free factorization; square-free number

Online: 19 February 2024 (07:58:05 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.0910.v1

On Generalized Fibospinomials: Generalized Fibonacci Polynomial Spinors

Ece Gulsah Colak, Nazmiye Gonul Bilgin, Yuksel Soykan

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: fibonacci numbers; fibonacci polynomials; fibonacci spinors; generalized fibonacci spinors; generalized fibonacci polynomial spinors

Online: 16 February 2024 (14:15:45 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202402.0842.v1

Exploring the Collatz Conjecture through Directed Graphs

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz Conjecture; Even Numbers; Odd Number; Directed Graphs

Online: 15 February 2024 (08:32:21 CET)

Show abstract| Download PDF| Share

Preprint ARTICLE | doi:10.20944/preprints202110.0087.v21

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sieve of eratosthenes; goldbach conjecture; polignac conjecture; twin prime conjecture

Online: 13 February 2024 (07:15:16 CET)

Show abstract| Download PDF| Share