论文标题
中央$ l $ l $ - 玛娜的形式的时刻
Moments of Central $L$-values for Maass Forms over Imaginary Quadratic Fields
论文作者
论文摘要
在本文中，在虚构的二次字段上，我们考虑了$ l $ functions $ l（s，f）$的家族，用于带有Archimedean参数$ t_f $的球形hecke-maass-maass forms $ f $。我们为中心价值的扭曲的第一和第二瞬间$ l \ big（\ frac 1 2，f \ big）$建立了渐近公式，可以证明至少$ 33 \％$ of $ l \ l \ big（\ frac 1 2，f \ f \ big）$ t_f \ leqslant $ non-inf $ t $ t $ t_f \ t $ t $ t $ t $ ty.我们的主要工具是kuznetsov球形痕迹公式和在虚二次磁场上的Voronoï求和公式。
In this paper, over imaginary quadratic fields, we consider the family of $L$-functions $L (s, f)$ for an orthonormal basis of spherical Hecke--Maass forms $f$ with Archimedean parameter $t_f$. We establish asymptotic formulae for the twisted first and second moments of the central values $L\big(\frac 1 2, f\big)$, which can be applied to prove that at least $33 \%$ of $L\big(\frac 1 2, f\big)$ with $t_f \leqslant T$ are non-vanishing as $T \rightarrow \infty$. Our main tools are the spherical Kuznetsov trace formula and the Voronoï summation formula over imaginary quadratic fields.
