论文标题
同时对静脉期和l功能的分数时刻
Simultaneous equidistribution of toric periods and fractional moments of L-functions
论文作者
论文摘要
圆环嵌入pGl（2）的内部形式中定义了圆环时期。杜克定理的一般版本指出，这一时期将其作为分裂场的判别倾向于无限。在本文中，我们将对角线嵌入的圆环中嵌入了PGL的两种不同的内部形式（2）。假设普遍的Riemann假设（以及一些其他技术假设），我们表现出同时的等分，因为判别倾向于无穷大，并具有有效的对数率。我们的证明是基于一种概率方法，用于估计由扩展的群体字符扭曲的L功能的分数矩。
The embedding of a torus into an inner form of PGL(2) defines an adelic toric period. A general version of Duke's theorem states that this period equidistributes as the discriminant of the splitting field tends to infinity. In this paper we consider a torus embedded diagonally into two distinct inner forms of PGL(2). Assuming the Generalized Riemann Hypothesis (and some additional technical assumptions), we show simultaneous equidistribution as the discriminant tends to infinity, with an effective logarithmic rate. Our proof is based on a probabilistic approach to estimating fractional moments of L-functions twisted by extended class group characters.
