L函数的复曲面周期和分数阶矩的同时等分布
Simultaneous equidistribution of toric periods and fractional moments of L-functions
摘要：
将环面嵌入到PGL（2）的内部形式中定义了一个椭圆环面周期。杜克定理的一般版本指出，当分裂场的判别式趋于无穷大时，这个周期均匀分布。本文考虑对角嵌入PGL（2）的两种不同内部形式的环面。假设广义黎曼假设（和一些额外的技术假设），我们同时等分布的判别趋于无穷大，有效的对数率。我们的证明是基于一个概率的方法来估计的分数阶矩的L函数扭曲的扩展类组字符。
英文摘要：
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.
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