Chinese Quarterly Journal of Mathematics ›› 2017, Vol. 32 ›› Issue (1): 16-33.doi: 10.13371/j.cnki.chin.q.j.m.2017.01.003

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Mean Values of the Hardy Sum

  

  1. School of Mathematics,Northwest University
  • Received:2015-11-06 Online:2017-03-30 Published:2020-10-26
  • About author:WANG Xiao-ying(1964-), female, native of Changwu, Shaanxi, a professor of Northwest University, Ph.D., engages in analytic number theory.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11571277); Supported by the Science and Technology Program of Shaanxi Province(2016GY-077);

Abstract: Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)j+1+[(hj)/p])from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions. 

Key words: Dedekind sum, Hardy sum, mean value, Dirichlet L-function

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