PGL（N）上Maass型Satake参数的加权Sato-Tate垂直分布
Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)
摘要：
本文给出了PGL（N）上的Maass型的傅里叶系数之间的一个严格的正交关系，其中N>=2.基于Golden-Kontorovich和Blomer对N=3的工作，以及我们对N>=4的猜想，我们证明了有限素数下Maass型的Satake参数的加权垂直等分布定理（关于广义Sato-Tate测度）.当N=3时，得到了等分布定理的收敛速率.
英文摘要：
We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the Satake parameter of Maass forms at a finite prime. For N=3, the rate of convergence for the equidistribution theorem is obtained.
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