On Selberg’s limit theorem for L-functions over a family of GL(n) Hecke–Maass cusp forms
On Selberg’s limit theorem for L-functions over a family of GL(n) Hecke–Maass cusp forms
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DOI：
10.1007/s11139-022-00590-4
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Guohua Chen;Y. Lau;Yingnan Wang
中科院分区：
文献类型：
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作者：
Guohua Chen;Y. Lau;Yingnan Wang
塞尔伯格极限定理断言，在适当的归一化下，临界线上的黎曼ζ函数的对数是正态分布的。Hejhal和Luo分别给出了一类GL（2）（GL（3））Hecke-Maass尖点形式虚部的谱模拟。Liu和Liu）使用Kuznetsov迹公式。本文利用Matz和Templier的自守Plancherel密度定理研究了GL（n）的情形。
The Selberg’s limit theorem asserts that under an appropriate normalization, the logarithm of the Riemann zeta-functionon the critical line is normally distributed. A spectral analog on the imaginary part ofover a family ofGL(2) (resp.GL(3)) Hecke–Maass cusp formsis developed by Hejhal and Luo (resp. Liu and Liu ) using the Kuznetsov trace formula. In this paper, we study the case ofGL(n),, with the automorphic Plancherel density theorem of Matz and Templier.