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arXiv · 2206.00434

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

Aditya Ghosh·Kobi Kremnizer·S. Waleed Noor·Charles F. Santos
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Abstract

In this article, we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function $\zeta$ 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 $\zeta$-function.

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Aditya Ghosh, Kobi Kremnizer, S. Waleed Noor, Charles F. Santos. 2022-05-17. Zero-free half-planes of the \zeta -function via spaces of analytic functions. https://doi.org/10.1016/j.aim.2024.109872

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