Congruences satisfied by eta-quotients

Ryan, Nathan; Scherr, Zachary; Sirolli, Nicolás; Treneer, Stephanie

doi:10.1090/proc/15293

Congruences satisfied by eta-quotients
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by Nathan C. Ryan, Zachary Scherr, Nicolás Sirolli and Stephanie Treneer PDF

Proc. Amer. Math. Soc. 149 (2021), 1039-1051 Request permission

Abstract:

The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general Fourier coefficients state the existence of infinitely many families of congruences. In this article we give an algorithm for computing explicit instances of such congruences for eta-quotients. We illustrate our method with a few examples.

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