# Extended-cycle integrals of modular functions for badly approximable numbers

@inproceedings{Murakami2021ExtendedcycleIO, title={Extended-cycle integrals of modular functions for badly approximable numbers}, author={Yuya Murakami}, year={2021} }

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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