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Equidistribution of higher dimensional generalized Dedekind sums and exponential sums

채희준|Jungyun Lee|전병흡
대한수학회 (The Korean Mathematical Society)|2020.07|대한수학회지 (Journal of the KMS)|제57권 제4호|pp. 845-871|DOI 10.4134/JKMS.j190406

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참고문헌

키워드

equidistributionTodd seriesgeneralized Dedekind sumsexponential sums
주제분류수학

초록

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 $\FR/\FZ$.

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 $\FR/\FZ$.

참고문헌 (24)

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