论文标题
扭曲的$ 2K $原始dirichlet $ l $ functions的矩：超越对角线
Twisted $2k$th moments of primitive Dirichlet $L$-functions: beyond the diagonal
论文作者
论文摘要
我们研究所有最多$ q $的所有原始字符字符的dirichlet $ l $ functions的家族，其中$ q $是一个倾向于$ \ infty $的参数。对于任意的正整数$ k $，我们使用dirichlet多项式近似$ l^k（s，χ）$长度$ x $的dirichlet多项式近似，并带有$ q <x <x <q^2 $。假设林达夫假设有广义，我们证明了这些扭曲力矩的近似值的渐近公式。我们的结果与Conrey，Farmer，Keating，Rubinstein和Snaith对这个$ L $ functions家族的预测一致，并为他们的猜想渐近公式提供了第一个严格的证据，以超越对角度的渐近公式，以供这个家庭的$ 2K $ $ THIM MINSEL。
We study the family of Dirichlet $L$-functions of all even primitive characters of conductor at most $Q$, where $Q$ is a parameter tending to $\infty$. For an arbitrary positive integer $k$, we approximate the twisted $2k$th moment of this family by using Dirichlet polynomial approximations of $L^k(s,χ)$ of length $X$, with $Q<X<Q^2$. Assuming the Generalized Lindelöf Hypothesis, we prove an asymptotic formula for these approximations of the twisted moments. Our result agrees with the prediction of Conrey, Farmer, Keating, Rubinstein, and Snaith for this family of $L$-functions, and provides the first rigorous evidence beyond the diagonal terms for their conjectured asymptotic formula for the general $2k$th moment of this family.
