Extended-cycle integrals of modular functions for badly approximable numbers
Number Theory
2022-11-03 v2 Dynamical Systems
Abstract
Cycle integrals of modular functions are expected to play a role in real quadratic analogue of singular moduli. In this paper, we extend the definition of cycle integrals of modular functions from real quadratic numbers to badly approximable numbers. We also give explicit representations of values of extended-cycle integrals for some cases.
Cite
@article{arxiv.2110.08452,
title = {Extended-cycle integrals of modular functions for badly approximable numbers},
author = {Yuya Murakami},
journal= {arXiv preprint arXiv:2110.08452},
year = {2022}
}
Comments
19 pages, 4 figures