A continuity of cycle integrals of modular functions
Number Theory
2019-11-12 v1
Abstract
In this paper we study a continuity of the "values" of modular functions at the real quadratic numbers which are defined in terms of their cycle integrals along the associated closed geodesics. Our main theorem reveals a more finer structure of the continuity of these values with respect to continued fraction expansions and it turns out that it is different from the continuity with respect to Euclidean topology.
Keywords
Cite
@article{arxiv.1911.03820,
title = {A continuity of cycle integrals of modular functions},
author = {Yuya Murakami},
journal= {arXiv preprint arXiv:1911.03820},
year = {2019}
}