Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.06.11
  • Accepted : 2019.09.11
  • Published : 2020.07.01
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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.

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Acknowledgement

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.

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