English

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.

Keywords

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

R2 v1 2026-06-24T06:56:12.611Z