Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers
Journal article, 2020

In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on nonholomorphic generating series. We establish a divisibility result for such nonholomorphic congruences of Hurwitz class numbers. The two key 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.


Olivia Beckwith

University of Illinois

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Olav K. Richter

University of North Texas

Proceedings of the National Academy of Sciences of the United States of America

0027-8424 (ISSN) 1091-6490 (eISSN)

Vol. 117 36 21953-21961

Subject Categories

Algebra and Logic


Discrete Mathematics





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