AI 中文总结
该研究针对r≥3的Hecke L-函数，利用多重Dirichlet级数理论，推导其在含2r次单位根的整体域上的扭曲矩渐近公式，证明其中心值存在正比例非零值。
AI 中文摘要
本文对包含2r次单位根的整体域上r阶（r≥3）Hecke L-函数的一阶和二阶扭曲矩建立渐近公式，主要聚焦代数数域。由此确定这类L-函数中心值存在正比例的非零值，具体针对无平方因子和r次无平方因子理想的族。我们的方法基于多重Dirichlet级数的理论框架。
英文摘要
In this paper, we establish asymptotic formulas for the first and second twisted moments of $r$-th order Hecke $L$-functions over global fields that contain the $2r$-th roots of unity, for $r\ge 3$. We focus primarily on algebraic number fields. As a consequence, we establish a positive proportion of non-vanishing central values for these $L$-functions, specifically for families of both square-free and $r$-th power-free ideals. Our approach is based on the machinery of multiple Dirichlet series.
Comments69 pages
