Zero-free half-planes of the ζ-function via spaces of analytic functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913489043324928 |
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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 |