On the logarithm of the Riemann zeta-function and its iterated integrals

Shōta Inoue

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arXiv · 1909.03643

On the logarithm of the Riemann zeta-function and its iterated integrals

Shōta Inoue

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Abstract

This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the value distribution of these functions and a relation between prime numbers and the distribution of zeros in short intervals.

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Shōta Inoue. 2019-09-09. On the logarithm of the Riemann zeta-function and its iterated integrals. https://arxiv.org/abs/1909.03643

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