Modularity of generating series of winding numbers
Number Theory
2017-11-27 v1
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.
Keywords
Cite
@article{arxiv.1711.08907,
title = {Modularity of generating series of winding numbers},
author = {Jan H. Bruinier and Jens Funke and Özlem Imamoglu and Yingkun Li},
journal= {arXiv preprint arXiv:1711.08907},
year = {2017}
}