journal6 ›› 2002, Vol. 23 ›› Issue (2): 52-55.

• Mathematics • Previous Articles     Next Articles

On the First Power Mean of Dirichlet L-FunctionsWith the Weight of Kloostermann Sums


  1. (Department of Math. and Com.,Yan'an University,Yanan 716000,Shanxi China)
  • Online:2002-06-15 Published:2013-01-05

Abstract: By using estimation of the classical kloostermann sum,estimation of the trigonomitric sum and the analytic method to study the first power mean of Dirichlet L-functions with the weight of general Kloostermann sum,a sharp asymptotic formula is given:∑x≠x0|S(m,n,x,q)|2|L(1,x)|=φ2(q)∑′∞n=1(r2(n))/(n2)+O(q3/2+ε).

Key words: Dirichlet L-functions, distribution of the mean value, general Kloostermann sum, asymptotic formula

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