On the density function for the value-distribution of automorphic L-functions

JOURNAL OF NUMBER THEORY

卷:198

Article

Matsumoto, Kohji¹  Umegaki, Yumiko² 

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Nara Womens Univ, Dept Phys & Math, Fac Sci, Courses Math, Nara 6308506, Japan

关键词: Automorphic L-function;    Value-distribution;    Density function;   

DOI  :  10.1016/j.jnt.2018.10.008

来源: Elsevier

【 摘 要 】

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 Gamma(0)(N). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free