Zagier's weight $3/2$ mock modular form

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.

A new lemma has been added, proofs of some of the lemmas have been corrected

References in corpus (2)

• Mock Theta Functions
• How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?