Modularity of generating series of winding numbers

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

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
• Public URL: https://durham-repository.worktribe.com/output/1370470