Lucas congruences using modular forms

Published 29 Aug 2024 in math.NT | (2408.16616v2)

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.

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