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Modularity of generating series of winding numbers

Modularity of generating series of winding numbers 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Modularity of generating series of winding numbers

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References (35)

Publisher
Springer Journals
Copyright
Copyright © 2018 by SpringerNature
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1007/s40687-018-0140-6
Publisher site
See Article on Publisher Site

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.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Apr 30, 2018

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