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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 $\FR/\FZ$.
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참고문헌 (24)
참고문헌 신청
T. M. Apostol / 1950 / Generalized Dedekind sums and transformation formulae of certain Lambert series / Duke Math. J. 17:147~157
M. Brion / 1997 / Lattice points in simple polytopes / J. Amer. Math. Soc 10(2):371~392
L. Carlitz / 1953 / Some theorems on generalized Dedekind sums / Pacic J. Math. 3:513~522
R. Chapman / 2000 / Reciprocity laws for generalized higher dimensional Dedekind sums / Acta Arith 93(2):189~199
R. Dedekind / 1892 / Riemann's Gesammelte Mathematische Werke
M. Brion / 1997 / Lattice points in simple polytopes / J. Amer. Math. Soc 10(2):371~392
L. Carlitz / 1953 / Some theorems on generalized Dedekind sums / Pacic J. Math. 3:513~522
R. Chapman / 2000 / Reciprocity laws for generalized higher dimensional Dedekind sums / Acta Arith 93(2):189~199
R. Dedekind / 1892 / Riemann's Gesammelte Mathematische Werke
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