Zero-free half-planes of the ζ-function via spaces of analytic functions

Fuente: arXiv
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Main Authors: Ghosh, Aditya, Kremnizer, Kobi, Noor, S. Waleed, Santos, Charles F.
Format: Preprint
Published: 2022
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author Ghosh, Aditya
Kremnizer, Kobi
Noor, S. Waleed
Santos, Charles F.
author_facet Ghosh, Aditya
Kremnizer, Kobi
Noor, S. Waleed
Santos, Charles F.
contents In this article, we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function $ζ$ by identifying topological vector spaces of analytic functions with specific properties. This approach is applied to weighted $\ell^2$ spaces and classical Hardy spaces $ H^p $ ($ 0<p\leq2 $). As a consequence precise conditions are obtained for the existence of zero-free half planes for the $ζ$-function.
format Preprint
id arxiv_https___arxiv_org_abs_2206_00434
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Zero-free half-planes of the ζ-function via spaces of analytic functions
Ghosh, Aditya
Kremnizer, Kobi
Noor, S. Waleed
Santos, Charles F.
Number Theory
Functional Analysis
In this article, we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function $ζ$ by identifying topological vector spaces of analytic functions with specific properties. This approach is applied to weighted $\ell^2$ spaces and classical Hardy spaces $ H^p $ ($ 0<p\leq2 $). As a consequence precise conditions are obtained for the existence of zero-free half planes for the $ζ$-function.
title Zero-free half-planes of the ζ-function via spaces of analytic functions
topic Number Theory
Functional Analysis
url https://arxiv.org/abs/2206.00434