An entire function defined by Riemann
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910505932685312 |
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| author | de Reyna, Juan Arias |
| author_facet | de Reyna, Juan Arias |
| contents | In one of the sheets in Riemann's Nachlass he defines an entire function and connect it with his zeta function. As in many pages in his Nachlass, Riemann is not giving complete proofs. However, I consider that this work is undoubtedly by Riemann. He obtains an $L^\infty$ function whose Fourier transform vanish at the real values $γ$ with $ζ(\frac12+iγ)=0$. We give proofs of Riemann formulas. This is an integral representation of the zeta function different from the known ones. I believe this is the first time it has been published. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An entire function defined by Riemann de Reyna, Juan Arias Number Theory History and Overview Primary 11M06, Secondary 30D99 In one of the sheets in Riemann's Nachlass he defines an entire function and connect it with his zeta function. As in many pages in his Nachlass, Riemann is not giving complete proofs. However, I consider that this work is undoubtedly by Riemann. He obtains an $L^\infty$ function whose Fourier transform vanish at the real values $γ$ with $ζ(\frac12+iγ)=0$. We give proofs of Riemann formulas. This is an integral representation of the zeta function different from the known ones. I believe this is the first time it has been published. |
| title | An entire function defined by Riemann |
| topic | Number Theory History and Overview Primary 11M06, Secondary 30D99 |
| url | https://arxiv.org/abs/2406.19717 |