Zero-free strips for the Riemann zeta-function derived from the Prime Number Theorem

Douglas Azevedo

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arXiv · 2012.09091

Zero-free strips for the Riemann zeta-function derived from the Prime Number Theorem

Douglas Azevedo

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Abstract

We use the Prime Number Theorem to prove the existence of zero-free strips for the Riemann-zeta function. Precisely, we prove that there exists $\delta>0$ for which if $0\leq r<\delta $ then $\zeta(s)\neq 0$ for Re$(s)>1-r$.

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Douglas Azevedo. 2020-12-16. Zero-free strips for the Riemann zeta-function derived from the Prime Number Theorem. https://arxiv.org/abs/2012.09091

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