English

Lucas congruences using modular forms

Number Theory 2024-10-24 v2

Abstract

In this work, we prove that many Ap\'ery-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.

Keywords

Cite

@article{arxiv.2408.16616,
  title  = {Lucas congruences using modular forms},
  author = {Frits Beukers and Wei-Lun Tsai and Dongxi Ye},
  journal= {arXiv preprint arXiv:2408.16616},
  year   = {2024}
}

Comments

This revision addresses the comments and suggestions provided by the referee