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arXiv · 1310.6374

New bounds for $\psi(x)$

Laura Faber·Habiba Kadiri
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Abstract

In this article we provide new explicit Chebyshev's bounds for the prime counting function $\psi(x)$. The proof relies on two new arguments: smoothing the prime counting function which allows to generalize the previous approaches, and a new explicit zero density estimate for the zeros of the Riemann zeta function.

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Laura Faber, Habiba Kadiri. 2013-10-23. New bounds for $\psi(x)$. https://arxiv.org/abs/1310.6374

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