Solutions to some sign change problems on functions involving sums of divisors

Συγγραφείς: Ding, Yuchen^{Aff1, IDs10998024006202_cor1}, Pan, Hao, Sun, Yu-Chen

Πηγή: Periodica Mathematica Hungarica. 90(2):299-306

Evaluation of the convolution sum ∑al+bm=nσ(l)σ3(m)(a,b)=(1,7),(7,1),(1,8),(8,1),(1,9),(9,1) for ∑al+bm=nσ(l)σ3(m)(a,b)=(1,7),(7,1),(1,8),(8,1),(1,9),(9,1) and representations by certain quadratic forms in twelve variables

Συγγραφείς: Alaca, Şaban, Kesicioğlu, Yavuz^{Aff2, IDs13226023004592_cor1}

Πηγή: Indian Journal of Pure and Applied Mathematics: Published by the Indian National Science Academy. 56(1):99-112

p-adic Valuation of the Sum of Divisors

Συγγραφείς: Zhao, Junjia, Chen, Yonggao^{Aff1, IDs1146402301542_cor1}

Πηγή: Frontiers of Mathematics. :1-33

Sums of divisors on arithmetic progressions

Συγγραφείς: Pongsriiam, Prapanpong^{Aff1, Aff2, IDs1099802300566x_cor1}

Πηγή: Periodica Mathematica Hungarica. 88(2):443-460

Some Equations Concerning the Sum of Divisors Function

Συγγραφείς: Dima, Andreea

Πηγή: The PUMP Journal of Undergraduate Research; Vol. 8 (2025): PUMP Journal of Undergraduate Research; 374-380 ; 2576-3725 ; 2765-8724

Θεματικοί όροι: equations, sum of divisors function, lifting the exponent lemma

Περιγραφή αρχείου: application/pdf

Relation: https://journals.calstate.edu/pump/article/view/6178/5080; https://journals.calstate.edu/pump/article/view/6178

Διαθεσιμότητα: https://journals.calstate.edu/pump/article/view/6178

Consolidated Proof of Robin's Inequality and the Riemann Hypothesis

Συγγραφείς: Polak, Robert

Θεματικοί όροι: Riemann hypothesis, Robin inequality, Highly composite numbers, Sum-of-divisors function, Chebyshev function, Mertens theorem, Rosser–Schoenfeld explicit bound, Robopol theorem, Analytic number theory, Numerical verification

Relation: https://zenodo.org/records/16785495; oai:zenodo.org:16785495; https://doi.org/10.5281/zenodo.16785495

Διαθεσιμότητα: https://doi.org/10.5281/zenodo.16785495
https://zenodo.org/records/16785495

From Trial Division to Smooth Prime Indicators: A Framework Based on Fourier Series

Συγγραφείς: Fuchs, Sebastian, orcid:0009-0009-1237-

Θεματικοί όροι: Prime numbers, sum-of-divisors function, tau function, analytic number theory, trigonometric series, Fejér kernel, sigma function

Relation: https://zenodo.org/records/15748475; oai:zenodo.org:15748475; https://doi.org/10.5281/zenodo.15748475

Διαθεσιμότητα: https://doi.org/10.5281/zenodo.15748475
https://zenodo.org/records/15748475

On Specially Multiplicative Functions

Συγγραφείς: Sivaraman, R, orcid:0000-0001-5989-, López-Bonilla, J, Morales-Cruz, D, Vidal-Beltrán, S

Θεματικοί όροι: Sum of divisors function, Recurrence relations, Ramanujan's tau function, Z-transform, Divisor function, Specially multiplicative function, Sequences of integers, Sum of squares, Alternating sum of divisors function

Relation: https://zenodo.org/communities/ejaset/; https://zenodo.org/records/10685964; oai:zenodo.org:10685964; https://doi.org/10.59324/ejaset.2024.2(1).03

Διαθεσιμότητα: https://doi.org/10.59324/ejaset.2024.2(1).03
https://zenodo.org/records/10685964

On Some Relations Involving the Ramanujan's Tau Function

Συγγραφείς: Dr. R. Sivaraman, orcid:0000-0001-5989-

Συνεισφορές: Dr. R. Sivaraman, Prof. J. López-Bonilla, S. Vidal Beltrán

Θεματικοί όροι: Sum of divisors function, Recurrence relations, Ramanujan's function 𝝉(𝒏), Bell polynomials, Chebyshev polynomials of the second kind

Relation: https://zenodo.org/records/11064259; oai:zenodo.org:11064259; https://doi.org/10.54105/ijam.A1168.04010424

Διαθεσιμότητα: https://doi.org/10.54105/ijam.A1168.04010424
https://zenodo.org/records/11064259

Ramanujan’s Tau-Function and Convolution Sums

Συγγραφείς: Sivaraman, R., López-Bonilla, J., Yaljá Montiel-Pérez, J.

Πηγή: European Journal of Theoretical and Applied Sciences; Vol. 2 No. 2 (2024): European Journal of Theoretical and Applied Sciences; 437-439 ; European Journal of Theoretical and Applied Sciences; Том 2 № 2 (2024): European Journal of Theoretical and Applied Sciences; 437-439 ; 2786-7447 ; 10.59324/ejtas.2024.2(2)

Θεματικοί όροι: Convolution sums, Sum of divisors function, Ramanujan’s function ττ(nn), Niebur’s formula, Lanphier’s identity

Περιγραφή αρχείου: application/pdf

Relation: https://ejtas.com/index.php/journal/article/view/781/578; https://ejtas.com/index.php/journal/article/view/781

Διαθεσιμότητα: https://ejtas.com/index.php/journal/article/view/781
https://doi.org/10.59324/ejtas.2024.2(2).37

The sum of divisors function and the Riemann hypothesis

Συγγραφείς: Jean-Louis Nicolas

Συνεισφορές: Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Combinatoire, théorie des nombres (CTN), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)

Πηγή: The Ramanujan Journal. 58:1113-1157

Θεματικοί όροι: Sum of divisors function, Superabundant number, Colossally abundant number, [MATH]Mathematics [math], 0101 mathematics, 01 natural sciences, Riemann hypothesis, Robin inequality

Σύνδεσμος πρόσβασης: https://link.springer.com/article/10.1007/s11139-021-00491-y

Robin Criterion on Divisibility

Συγγραφείς: Vega, Frank

Πηγή: The Ramanujan Journal. 59:745-755

Θεματικοί όροι: sum-of-divisors function, prime numbers, 0101 mathematics, 01 natural sciences, Riemann hypothesis, Robin inequality

Σύνδεσμος πρόσβασης: https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/61158452abc9e239046c162b/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/60fed97a393cc9d0634f0acc/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6110834f30231a196f0651a5/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/60a338e2481359a8495252a5/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/60c81fbfbb8c1ab1e83dce4e/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/61eb90358d70c31cbf09c413/original/robin-s-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/60fbbbac8804439fb8e33763/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/61134722abc9e20d306ae1d0/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/61532c88b19c7ef331e29776/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6167c6487d3da52a62f748d5/original/robin-criterion-on-divisibility.pdf
https://www.cambridge.org/engage/coe/article-details/60c81fbfbb8c1ab1e83dce4e

Robin’s criterion on divisibility

Συγγραφείς: Vega, Frank

Πηγή: The Ramanujan Journal: An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan. 59(3):745-755

SUM OF DIVISORS FUNCTION

Συγγραφείς: R. Sivaraman, J. D. Bulnes, J. López-Bonilla

Πηγή: INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH. 11

Θεματικοί όροι: Sum of divisors function, Bell polynomials, Sums of triangular numbers, Recurrence relations, Osler et al - Robbins identity, Colour partitions, Pentagonal numbers, Partition function, 0101 mathematics, 01 natural sciences

On Solé and Planat criterion for the Riemann Hypothesis

Συγγραφείς: Vega, Frank

Θεματικοί όροι: Prime numbers, 0101 mathematics, Superabundant numbers, 01 natural sciences, Sum-of-divisors function, Riemann hypothesis

Robin’s Criterion on Superabundant Numbers

Συγγραφείς: Vega, Frank

Θεματικοί όροι: Robin's inequality, Prime numbers, Superabundant numbers, Sum-of-divisors function, Riemann hypothesis

A Very Brief Note on the Riemann Hypothesis

Συγγραφείς: Vega, Frank

Συνεισφορές: Vega, Frank

Θεματικοί όροι: Robin's inequality, Prime numbers, Superabundant numbers, Riemann Hypothesis, Sum-of-divisors function, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

Περιγραφή αρχείου: application/pdf

Σύνδεσμος πρόσβασης: https://hal.science/hal-03744533v4

On the Polynomial Structure of 𝒓𝒌(𝒏)

Συγγραφείς: Dr. R. Sivaraman, orcid:0000-0001-5989-

Συνεισφορές: Dr. R. Sivaraman, Prof. J. López-Bonilla, S. Vidal-Beltrán, ESIME-Zacatenco

Θεματικοί όροι: Sum of Divisors Function, Sequences of Integers, Sums of Squares, Recurrence Relations

Relation: https://zenodo.org/records/10440740; oai:zenodo.org:10440740; https://doi.org/10.54105/ijam.A1162.103223

Διαθεσιμότητα: https://doi.org/10.54105/ijam.A1162.103223
https://zenodo.org/records/10440740

Ramanujan's Tau-Function in Terms of Bell Polynomials

Συγγραφείς: Dr. R. Sivaraman, orcid:0000-0001-5989-

Συνεισφορές: Dr. R. Sivaraman, H. N. Núñez-Yépez, Prof. J. López-Bonilla

Θεματικοί όροι: Sum of divisors function, Color partitions, Recurrence relations, Complete Bell polynomials, Ramanujan's function 𝝉(𝒏)

Relation: https://zenodo.org/records/10049544; oai:zenodo.org:10049544; https://doi.org/10.54105/ijam.B1157.103223

Διαθεσιμότητα: https://doi.org/10.54105/ijam.B1157.103223
https://zenodo.org/records/10049544

Complete Bell Polynomials and Recurrence Relations for Arithmetic Functions

Συγγραφείς: Ramaswamy Sivaraman, orcid:0000-0001-5989-, Juan José Díaz Bulnes, Jose Luis López-Bonilla

Θεματικοί όροι: sum of divisors function, Z-transform, sums of squares, color partitions, recurrence relations, sums of triangular numbers, bell polynomials, sum of inverses of odd divisors of an integer

Relation: https://zenodo.org/communities/ejtas/; https://zenodo.org/records/8087426; oai:zenodo.org:8087426; https://doi.org/10.59324/ejtas.2023.1(3).18

Διαθεσιμότητα: https://doi.org/10.59324/ejtas.2023.1(3).18
https://zenodo.org/records/8087426