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http://dx.doi.org/10.4134/JKMS.j190406

EQUIDISTRIBUTION OF HIGHER DIMENSIONAL GENERALIZED DEDEKIND SUMS AND EXPONENTIAL SUMS  

Chae, Hi-joon (Department of Mathematics Education Hongik University)
Jun, Byungheup (Department of Mathematical Sciences Ulsan National Institute of Science and Technology)
Lee, Jungyun (Department of Mathematics Education Kangwon National University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 845-871 More about this Journal
Abstract
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 ℝ/ℤ.
Keywords
generalized Dedekind sums; Todd series; exponential sums; equidistribution;
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