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arXiv · 2110.08452

Extended-cycle integrals of modular functions for badly approximable numbers

Yuya Murakami
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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.

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Yuya Murakami. 2021-10-16. Extended-cycle integrals of modular functions for badly approximable numbers. https://arxiv.org/abs/2110.08452

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