Zagier's weight $3/2$ mock modular form
Number Theory
2022-05-19 v2
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 for the discriminant . In the modern framework, these results show that the generating function of 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.
Keywords
Cite
@article{arxiv.2012.00539,
title = {Zagier's weight $3/2$ mock modular form},
author = {Ajit Bhand and Ranveer Kumar Singh},
journal= {arXiv preprint arXiv:2012.00539},
year = {2022}
}
Comments
A new lemma has been added, proofs of some of the lemmas have been corrected