Modularity of generating series of winding numbers

Bruinier, J.; Funke, J.; Imamoḡlu, Ö; Li, Y.

doi:10.1007/s40687-018-0140-6

Modularity of generating series of winding numbers

Bruinier, J.; Funke, J.; Imamoḡlu, Ö; Li, Y.

Authors

J. Bruinier

Professor Jens Funke jens.funke@durham.ac.uk
Professor

Ö Imamoḡlu

Y. Li

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.

Citation

Bruinier, J., Funke, J., Imamoḡlu, Ö., & Li, Y. (2018). Modularity of generating series of winding numbers. Research in the Mathematical Sciences, 5(2), Article 23. https://doi.org/10.1007/s40687-018-0140-6

Journal Article Type	Article
Acceptance Date	Apr 17, 2018
Online Publication Date	Apr 30, 2018
Publication Date	Apr 30, 2018
Deposit Date	Nov 28, 2017
Publicly Available Date	Apr 30, 2019
Journal	Research in the Mathematical Sciences
Print ISSN	2522-0144
Electronic ISSN	2197-9847
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	5
Issue	2
Article Number	23
DOI	https://doi.org/10.1007/s40687-018-0140-6