Sequences, modular forms and cellular integrals

Dermot McCarthy; Robert Osburn; Armin Straub

Sequences, modular forms and cellular integrals

Dermot McCarthy, Robert Osburn, Armin Straub

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

It 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.

MSC Codes 11F03 (Primary), 11M32, 14H10 (Secondary)

Original language	English
Journal	Unknown Journal
State	Published - May 16 2017

Keywords

Modular forms
Period integrals
Supercongruences

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title = "Sequences, modular forms and cellular integrals",

abstract = "It is well-known that the Ap{\'e}ry 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.MSC Codes 11F03 (Primary), 11M32, 14H10 (Secondary)",

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AU - McCarthy, Dermot

AU - Osburn, Robert

AU - Straub, Armin

PY - 2017/5/16

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N2 - It 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.MSC Codes 11F03 (Primary), 11M32, 14H10 (Secondary)

AB - It 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.MSC Codes 11F03 (Primary), 11M32, 14H10 (Secondary)

KW - Modular forms

KW - Period integrals

KW - Supercongruences

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M3 - Article

AN - SCOPUS:85094245624

JO - Unknown Journal

JF - Unknown Journal

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