Bounding the integral of the argument of the Riemann Zeta function

Victor Amberger

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arXiv · 2512.23064

Bounding the integral of the argument of the Riemann Zeta function

Victor Amberger

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Abstract

This article improves the estimate of $|S_1(t_2)-S_1(t_1)|$, which is the definite integral of the argument of the Riemann zeta-function between $t_1$ and $t_2$. Estimates of this quantity are needed to apply Turing's method to compute the exact number of zeta zeros up to a given height.

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Victor Amberger. 2025-12-28. Bounding the integral of the argument of the Riemann Zeta function. https://arxiv.org/abs/2512.23064

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