J. Korean Math. Soc. 2020; 57(4): 845-871
Published online July 1, 2020 https://doi.org/10.4134/JKMS.j190406
Copyright © The Korean Mathematical Society.
Hi-joon Chae, Byungheup Jun, Jungyun Lee
Hongik University; Ulsan National Institute of Science and Technology; Kangwon National University
We consider generalized Dedekind sums in dimension $n$, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in $\FR/\FZ$.
Keywords: generalized Dedekind sums, Todd series, exponential sums, equidistribution
MSC numbers: 11F20, 11L03, 14M25
Supported by: The first author was supported by 2019 Hongik University Research Fund.
The second author was supported by NRF-2018R1D1A1A02085748.
The third author was supported by 2019 Research Grant from Kangwon National University and NRF-2017R1A6A3A11030486.
2006; 43(1): 111-131
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