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Modularity of generating series of winding numbers.

Bruinier, J. and Funke, J. and Imamoḡlu, Ö. and Li, Y. (2018) 'Modularity of generating series of winding numbers.', Research in the mathematical sciences., 5 (2). p. 23.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Date accepted:17 April 2018
Date deposited:25 April 2018
Date of first online publication:30 April 2018
Date first made open access:30 April 2019

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