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Mathematics > Number Theory

arXiv:1805.11072 (math)
[Submitted on 28 May 2018 (v1), last revised 9 Jul 2021 (this version, v3)]

Title:On certain mean values of logarithmic derivatives of $L$-functions and the related density functions

Authors:Masahiro Mine
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Abstract:We study some "density function" related to the value-distribution of $L$-functions. The first example of such a density function was given by Bohr and Jessen in 1930s for the Riemann zeta-function. In this paper, we construct the density function in a wide class of $L$-functions. We prove that certain mean values of $L$-functions in the class are represented as integrals involving the related density functions.
Comments: 19 pages
Subjects: Number Theory (math.NT)
MSC classes: 11M41(Primary), 11R42(Secondary)
Cite as: arXiv:1805.11072 [math.NT]
  (or arXiv:1805.11072v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.11072
Journal reference: Funct. Approx. Comment. Math. 61 (2019) 179-199
Related DOI: https://doi.org/10.7169/facm/1770

Submission history

From: Masahiro Mine [view email]
[v1] Mon, 28 May 2018 17:30:57 UTC (14 KB)
[v2] Wed, 12 Sep 2018 00:23:37 UTC (14 KB)
[v3] Fri, 9 Jul 2021 07:06:31 UTC (15 KB)
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