Mock Modular Forms and Class Number Relations

TL;DR

This paper proves a long-standing conjecture by H. Cohen about the generating function of Hurwitz class numbers using mock modular forms, revealing numerous new class number relations.

Contribution

It introduces a novel proof of Cohen's conjecture employing mock modular forms, establishing new infinite class number relations.

Findings

Proves Cohen's conjecture on Hurwitz class numbers

Derives infinite unproven class number relations

Advances understanding of mock modular forms' role in number theory

Abstract

In this paper, we prove an almost 40 year old conjecture by H. Cohen concerning the generating function of the Hurwitz class number of quadratic forms using the theory of mock modular forms. This conjecture yields an infinite number of so far unproven class number relations.