Congruences of Hurwitz class numbers on square classes
Journal article, 2022

We extend a holomorphic projection argument of our earlier work to prove a novel divisibility result for non-holomorphic congruences of Hurwitz class numbers. This result allows us to establish Ramanujan-type congruences for Hurwitz class numbers on square classes, where the holomorphic case parallels previous work by Radu on partition congruences. We offer two applications. The first application demonstrates common divisibility features of Ramanujan-type congruences for Hurwitz class numbers. The second application provides a dichotomy between congruences for class numbers of imaginary quadratic fields and Ramanujan-type congruences for Hurwitz class numbers.

Holomorphic projection

Hurwitz class numbers

Ramanujan-type congruences


Olivia Beckwith

Tulane University

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

Olav K. Richter

University of North Texas

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 409 108663

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Subject Categories

Algebra and Logic


Mathematical Analysis



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