Year: 2020
Type: preprint
Abstract: Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating function of the Hurwitz class numbers $H(n)$ for the discriminant $(-n)$. In the modern framework, these results show that the generating function of $H(n)$ is a mock modular form of weight 3/2 with the theta function being the shadow. In this expository paper, we provide a detailed proof of Zagier's result.
Source: arXiv (Cornell University)
Authors: Bhand, Ajit, Singh, Ranveer Kumar
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3106824243