Korean J. Math. Vol. 23 No. 4 (2015) pp.571-590
DOI: https://doi.org/10.11568/kjm.2015.23.4.571

Mean values of the homogeneous Dedekind sums

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Published: Dec 30, 2015
Keywords:
Dedekind sum, character sum, Dirichlet L-functionm mean value
Mathematics Subject Classification:
11F20

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Xiaoying Wang
School of Mathematics Northwest University Xi'an 710127, Shaanxi, P. R. China
Xiaxia Yue
School of Mathematics Northwest University Xi'an 710127, Shaanxi, P. R. China

Abstract

Let a, b, q be integers with q>0. The homogeneous Dedekind sum is defined by
S(a,b,q)=∑r=1q((arq))((brq)),
where
((x))={x−[x]−12,if x is not an integer,0,if x is an integer.
In this paper we study the mean value of S(a,b,q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.



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Supporting Agencies

This work was supported by the Science and Technology Program of Shaanxi Province of China under Grant No. 2013JM1017.

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