Sequences, modular forms and cellular integrals-Reference-Cited by-同舟云学术

Sequences, modular forms and cellular integrals

Published:2018-10-11 Issue:2 Volume:168 Page:379-404
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

McCARTHY DERMOT,OSBURN ROBERT,STRAUB ARMIN

Abstract

AbstractIt is well-known that the Apéry sequences which arise in the irrationality proofs for ζ(2) and ζ(3) satisfy many intriguing arithmetic properties and are related to the pth Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference43 articles.

1. On the Picard-Fuchs equation and the formal brauer group of certain ellipticK3-surfaces

2. R. Osburn and A. Straub Interpolated sequences and critical $L$-values of modular forms. Preprint (2018), arXiv:1806.05207

3. Supercongruences for Apéry-like numbers

4. Congruences via modular forms

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On sporadic sequences;Monatshefte für Mathematik;2024-06-07

2. On three conjectural congruences of Z.-H. Sun involving Apéry and Apéry-like numbers;Monatshefte für Mathematik;2023-03-20

3. Generalized Paley graphs and their complete subgraphs of orders three and four;Research in the Mathematical Sciences;2021-03-09

4. Congruences involving binomial coefficients and Apery-like numbers;Publicationes Mathematicae Debrecen;2020-04-01

5. Some numeric hypergeometric supercongruences;Vertex Operator Algebras, Number Theory and Related Topics;2020