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

Ajit Bhand; Ranveer Kumar Singh

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arXiv · 2012.00539

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

Ajit Bhand·Ranveer Kumar Singh

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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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Ajit Bhand, Ranveer Kumar Singh. 2020-12-01. Zagier's weight $3/2$ mock modular form. https://arxiv.org/abs/2012.00539

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