Equidistribution of higher dimensional generalized Dedekind sums and exponential sums
J. Korean Math. Soc.
Published online November 7, 2019
Hi-joon Chae, Byungheup Jun, and Jungyun Lee
Hongik University, UNIST, Kangwon National University
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
MSC numbers : 11F20, 11L03, 14M25
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