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arXiv · 1805.11066

The density function for the value-distribution of the Lerch zeta-function and its applications

Masahiro Mine
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Abstract

The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure related to the value-distribution of the Lerch zeta-function. We prove that it has a density function which we can explicitly construct. Moreover, we prove an asymptotic formula for the number of zeros of the Lerch zeta-function on the right side of the critical line, whose main term is associated with the density function.

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Masahiro Mine. 2018-05-28. The density function for the value-distribution of the Lerch zeta-function and its applications. https://doi.org/10.1307/mmj%2F1586570481

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