算术函数的局部性质及其在自守L函数中的应用
Local Behavior of Arithmetical Functions with Applications to Automorphic L-Functions
摘要：
本文给出了一类算术函数的局部加权均值的Voronoi型级数逼近，该算术函数与满足带Gamma因子的函数方程的狄利克雷级数相关联.利用Heath-Brown和Tsang [7]的方法，利用该序列来研究振荡频率。一个副产品是另一个证明的著名结果没有元素在塞尔伯格类的程度0 \textless{} d \textless{} 1。我们的主要应用包括GL m的自守L函数的系数的变号问题，它改进了Liu和Wu [14]的一些结果.半整权的模形式和Siegel特征形的情况也被考虑。
英文摘要：
We derive a Voronoi-type series approximation for the local weighted mean of an arithmetical function that is associated to Dirichlet series satisfying a functional equation with gamma factors. The series is exploited to study the oscillation frequency with a method of Heath-Brown and Tsang [7]. A by-product is another proof for the well-known result of no element in the Selberg class of degree 0 \textless{} d \textless{} 1. Our major applications include the sign-change problem of the coefficients of automorphic L-functions for GL m , which improves significantly some results of Liu and Wu [14]. The cases of modular forms of half-integral weight and Siegel eigenforms are also considered.
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