• Title/Summary/Keyword: Dirichlet L-functionm mean value

Search Result 1, Processing Time 0.017 seconds

MEAN VALUES OF THE HOMOGENEOUS DEDEKIND SUMS

  • WANG, XIAOYING;YUE, XIAXIA
    • Korean Journal of Mathematics
    • /
    • v.23 no.4
    • /
    • pp.571-590
    • /
    • 2015
  • Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ 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.