@article{34ec1998242c460daa928c73b32b1d30,
title = "Arithmetic of generalized dedekind sums and their modularity",
abstract = "Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ℚdefined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.",
keywords = "Dedekind sum, Quantum modular form",
author = "Dohoon Choi and Byungheup Jun and Jungyun Lee and Subong Lim",
note = "Funding Information: The second named author was supported by (NRF-2015R1D1A1A09059083) Funding Information: The second named author was supported by (NRF-2015R1D1A1A09059083) and the third named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827) and (NRF-2017R1A6A3A11030486) and the last author was supported by (NRF-2017R1C1B5017409). Publisher Copyright: {\textcopyright} 2018 Choi et al., published by De Gruyter. 2018.",
year = "2018",
doi = "10.1515/math-2018-0082",
language = "English",
volume = "16",
pages = "967--985",
journal = "Open Mathematics",
issn = "1895-1074",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "1",
}