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arXiv · 1711.08907

Modularity of generating series of winding numbers

Jan H. Bruinier·Jens Funke·Özlem Imamoglu·Yingkun Li
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Abstract

The Shimura correspondence connects modular forms of integral weights and half-integral weights. One of the directions is realized by the Shintani lift, where the inputs are holomorphic differentials and the outputs are holomorphic modular forms of half-integral weight. In this article, we generalize this lift to differentials of the third kind. As an application we obtain a modularity result concerning the generating series of winding numbers of closed geodesics on the modular curve.

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Jan H. Bruinier, Jens Funke, Özlem Imamoglu, Yingkun Li. 2017-11-24. Modularity of generating series of winding numbers. https://arxiv.org/abs/1711.08907

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