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arXiv · 1805.11072

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

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.

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Masahiro Mine. 2018-05-28. On certain mean values of logarithmic derivatives of $L$-functions and the related density functions. https://doi.org/10.7169/facm%2F1770

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