Dirichlet L-函数倒数的2k次加权均值

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

利用三角和估计、特征和估计与解析方法,研究DirichletL-函数倒数的2k次加权均值.证明了当整数q≥2,实数Q>1时,对任意的正整数k和m,且(m, q≤Qq)=1,有加权均值公式 q≤QAk(q)φ2(q) xmodq｜G(m,q)｜2｜L(1,x)｜2k=(15π2)kQ+O(Q12+ε).

This paper uses estimation of the trigonomitric sums and character sums and the analytic method to study the 2k-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≤QAk(q)φ2(q)xmod q|G(m,q)|2|L(1,x)|2k=(15π2)kQ+O(Q12+ε).