Congruences satisfied by eta-quotients

Nathan C. Ryan, Zachary Scherr, Nicolás Sirolli, Stephanie Treneer

Published 2019-11-13Version 1

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.