Zagier's weight 3/2 mock modular form

2020/12/01 by Bhand, Ajit, Singh, Ranveer Kumar
#11F03 #11F37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2012.00539

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.

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