On the density function for the value-distribution of automorphic L-functions
On the density function for the value-distribution of automorphic L-functions
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关于自守 L 函数值分布的密度函数
DOI：
10.1016/j.jnt.2018.10.008
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发表时间：
2019
影响因子：
0.7
通讯作者：
Kohji Matsumoto and Yumiko Umegaki
中科院分区：
文献类型：
--
作者：
Nose;M.;and Y. Murayama;Kohji Matsumoto and Yumiko Umegaki
Abstract The Bohr–Jessen limit theorem is a probabilistic limit theorem on the value-distribution of the Riemann zeta-function in the critical strip. Moreover their limit measure can be written as an integral involving a certain density function. The existence of the limit measure is now known for a quite general class of zeta-functions, but the integral expression has been proved only for some special cases (such as Dedekind zeta-functions). In this paper we give an alternative proof of the existence of the limit measure for a general setting, and then prove the integral expression, with an explicitly constructed density function, for the case of automorphic L-functions attached to primitive forms with respect to congruence subgroups Γ 0 (N).
