journal6 ›› 2003, Vol. 24 ›› Issue (2): 43-46.

• Mathematics • Previous Articles     Next Articles

On the 2k-th Power Mean of the Inversion of DirichletL-Function With the Weight of Gauss Sums


  1. (The Department of Math.,Yan'an University,Yan'an 716000,Shanxi China)
  • Online:2003-06-15 Published:2012-11-07

Abstract: This paper uses estimation of the trigonomitric sums and character sums and the analytic method to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of Gauss sums.It is proved that when integer q≥2,real number Q>1,for the arbitrary positive integers k and m,and (m,q≤Qq)=1,the power mean value formula is given as:q≤Q(Ak(q))/(φ2(q))xmod q(|G(m,q)|2)/(|L(1,x)|2k)=(15/π2)kQ+O(Q1/2+ε).

Key words: Dirichlet L-functions, character sums, distribution of the mean value, Gauss sums

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