On the exact location of the non-trivial zeros of Riemann’s zeta function
In this paper we introduce the real valued real analytic function κ(t) implicitly defined by e 2πiκ(t) = −e −2iϑ(t) ζ 0 ( 1 2 − it) ζ 0( 1 2 + it) , (κ(0) = − 1 2 ). By studying the equation κ(t) = n (without making any unproved hypotheses), we will show that (and how) this function is closely relat...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43000 |
| Acceso en línea: | http://hdl.handle.net/11441/43000 https://doi.org/10.4064/aa163-3-3 |
| Access Level: | acceso abierto |
| Palabra clave: | Zeta function Non-trivial zeros Distribution of zeros |
| Sumario: | In this paper we introduce the real valued real analytic function κ(t) implicitly defined by e 2πiκ(t) = −e −2iϑ(t) ζ 0 ( 1 2 − it) ζ 0( 1 2 + it) , (κ(0) = − 1 2 ). By studying the equation κ(t) = n (without making any unproved hypotheses), we will show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ 0 (s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it will follow that the ordinate of the zero 1/2 + iγn of ζ(s) will be the unique solution to the equation κ(t) = n. |
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