Dirichlet L-函数的二次加权均值分布

On the Second Power Mean Distribution of Dirichlet L-functions

利用三角和估计、特征和估计等解析方法研究 Dirichlet L -函数的二次加权均值分布 ,得出均值分布的渐近公式∑χ≠χ0|G(m,χ) |2 |L (1,χ) |2 =π26 φ2 (q) ∏p| q1- 1p2 +O q32 ln2 qd(q) .

The second power mean distribution of Dirichlet L-functions is studied by using some analytic methods such as estimation of trigonometric sum,estimation of character sum ect..Its asymptotic formula is given as follows: ∑χ≠χ 0|G(m,χ)|2|L(1,χ)|2=π26φ2(q)∏p|q1-1p2+Oq 32ln2qd(q).