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arXiv · 2403.03301

Supercongruences using modular forms

Frits Beukers
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Abstract

Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very often these congruences turn out to hold modulo $p^2$ or even $p^3$. We call such congruences supercongruences and in the past 15 years an abundance of them have been discovered. In this paper we show that a large proportion of them can be explained by the use of modular functions and forms.

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Frits Beukers. 2025-06-16. Supercongruences using modular forms. https://arxiv.org/abs/2403.03301

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