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arXiv · 1912.00853

Oscillations of the error term in the prime number theorem

Jan-Christoph Schlage-Puchta
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Abstract

Let $\sigma+i\gamma$ be a zero of the Riemann zeta function to the right of the line $\frac{1}{2}+it$. We show that this zero causes large oscillations of the error term of the prime number theorem. Our result is close to optimal both in terms of the magnitude and in the localization of large values for the error term.

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Jan-Christoph Schlage-Puchta. 2019-12-02. Oscillations of the error term in the prime number theorem. https://arxiv.org/abs/1912.00853

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