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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 p² or even p³. 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.
Frits Beukers (Tue,) studied this question.
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