2024-03-02T23:44:30Z
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2023-01-16T04:20:44Z
697:698:699
On the density function for the value-distribution of automorphic L-functions
Matsumoto, Kohji
92175
Umegaki, Yumiko
92176
Automorphic L-function
Value-distribution
Density function
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 Γ0(N).
ファイル公開：2021-05-01
journal article
Elsevier
2019-05
application/pdf
Journal of Number Theory
198
176
199
0022-314X
https://nagoya.repo.nii.ac.jp/record/28255/files/Matsumoto-Umegaki-revised.pdf
eng
https://doi.org/10.1016/j.jnt.2018.10.008
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/