论文标题
二次dirichlet $ l $ functions在功能字段上
Mollified moments of quadratic Dirichlet $L$-functions over function fields
论文作者
论文摘要
我们为功能场设置中的Quadratic dirichlet $ l $ functions的家族的第一和第二瞬间计算渐近公式。作为一个应用程序，我们在中央点$ s = 1/2 $的完整$ l $ functions $λ（s，χ_d）$的衍生物中获得了非变化结果。特别是，我们表明$λ^{（2K）}（\ frac {1} {2}，χ_d）\ neq 0 $的比例为$ 1+o（k^{ - 2}）$ as $ k \ to \ to \ infty $。
We compute asymptotic formulae for the mollified first and second moments for the family of quadratic Dirichlet $L$-functions in the function field setting. As an application, we obtain non-vanishing results for the derivatives of the completed $L$-functions $Λ(s,χ_D)$ at the central point $s=1/2$. In particular, we show that the proportion of $Λ^{(2k)}(\frac{1}{2},χ_D) \neq 0$ is $1+O(k^{-2})$ as $k \to \infty$.
