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arXiv · 2311.04347

A smooth version of Landaus explicit formula

Eugenio P. Balanzario·Daniel Eduardo Cardenas Romero·Richar Chacon Serna
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Abstract

We present a smooth version of Landaus explicit formula for the von Mangoldt arithmetical function. Assuming the validity of the Riemann hypothesis, we show that in order to determine whether a natural number is a prime number, it is sufficient to know the location of a number of non trivial zeros of the Riemann zeta function. Next we use Heisenbergs inequality to support the conjecture that this number of zeros cannot be essentially diminished

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Eugenio P. Balanzario, Daniel Eduardo Cardenas Romero, Richar Chacon Serna. 2023-11-07. A smooth version of Landaus explicit formula. https://arxiv.org/abs/2311.04347

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