Congruences satisfied by eta-quotients
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.
Cite
@article{arxiv.1911.05799,
title = {Congruences satisfied by eta-quotients},
author = {Nathan C. Ryan and Zachary Scherr and Nicolás Sirolli and Stephanie Treneer},
journal= {arXiv preprint arXiv:1911.05799},
year = {2023}
}
Comments
Corrected version. A small error in the code (the wrong C type was used for part of the computation) led us to find that certain candidates which were claimed to be uninteresting in the paragraph following Proposition 5.2 in the previous version are actually interesting. We have changed the paragraph accordingly but have left Proposition 5.2 intact