Lucas congruences using modular forms

Frits Beukers; Wei Lun Tsai; Dongxi Ye

doi:10.1112/blms.13182

Lucas congruences using modular forms

Frits Beukers, Wei Lun Tsai, Dongxi Ye^*

^*Corresponding author for this work

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

Abstract

In this work, we prove that many Apéry-like sequences arising from modular forms satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm four conjectural Lucas congruences that were recently posed by S. Cooper and reinterpret a number of known results.

Original language	English
Pages (from-to)	69-78
Number of pages	10
Journal	Bulletin of the London Mathematical Society
Volume	57
Issue number	1
Early online date	12 Nov 2024
DOIs	https://doi.org/10.1112/blms.13182
Publication status	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

Funding

We thank the referee for the very helpful comments, suggestions, and corrections, which have definitely improved the manuscript.

Funders	Funder number
AMS-Simons Travel Grant

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10.1112/blms.13182

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Lucas congruences using modular forms

Abstract

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