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arXiv · 2402.04272

On the error term in the explicit formula of Riemann-von Mangoldt II

Michaela Cully-Hugill·Daniel R. Johnston
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Abstract

We give an explicit $O(x/T)$ error term for the truncated Riemann--von Mangoldt explicit formula. For large $x$, this provides a modest improvement over previous work, which we demonstrate via an application to a result on primes between consecutive powers.

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Michaela Cully-Hugill, Daniel R. Johnston. 2024-02-01. On the error term in the explicit formula of Riemann-von Mangoldt II. https://arxiv.org/abs/2402.04272

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