Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers
Number Theory
2022-05-25 v2
Abstract
In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on non-holomorphic generating series. We establish a divisibility result for such non-holomorphic congruences of Hurwitz class numbers. The two keys tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.
Cite
@article{arxiv.2004.06886,
title = {Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers},
author = {Olivia Beckwith and Martin Raum and Olav K. Richter},
journal= {arXiv preprint arXiv:2004.06886},
year = {2022}
}