Generating Functions of the Hurwitz Class Numbers Associated with Certain Mock Theta Functions

TL;DR

This paper derives series representations for generating functions of Hurwitz class numbers related to mock theta functions and provides combinatorial interpretations, enhancing understanding of their structure and connections.

Contribution

It introduces new Hecke-Rogers type series for Hurwitz class numbers and offers combinatorial interpretations, linking class numbers to mock theta functions.

Findings

Series representations closely related to mock theta functions

Two combinatorial interpretations of Hurwitz class numbers

Deeper understanding of the structure of Hurwitz class numbers

Abstract

We find the Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which is very close to certain mock theta functions. We also prove two combinatorial interpretation of Hurwitz class numbers appeared on OEIS.