Majoration du nombre de zéros d'une fonction méromorphe en dehors d'une droite verticale et applications
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | VELÁSQUEZ CASTAÑÓN, Oswaldo | |
| dc.date.accessioned | 2024-04-04T03:03:28Z | |
| dc.date.available | 2024-04-04T03:03:28Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193074 | |
| dc.description.abstractEn | We study the distribution of the zeros of functions of the form $f(s)=h(s) \pm h(2a-s)$, where $h(s)$ is a meromorphic function, real on the real line, $a$ a real number. One of our results establishes sufficient conditions under which all but finitely many of the zeros of $f(s)$ lie on the line $\Re s = a$, called the {\it critical line} for the function $f(s)$, and be simple, given that all but finitely many of the zeros of $h(s)$ lie on the half-plane $\Re s < a$. This results can be regarded as a generalization of the necessary condition of stability for the function $h(s)$, in the Hermite-Biehler theorem. We apply this results to the study of translations of the Riemann Zeta Function and $L$ functions, and integrals of Eisenstein Series, among others. | |
| dc.language.iso | fr | |
| dc.subject.en | Riemann Hypothesis | |
| dc.subject.en | Stability | |
| dc.subject.en | Hermite-Biehler Theorem | |
| dc.title | Majoration du nombre de zéros d'une fonction méromorphe en dehors d'une droite verticale et applications | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 0712.1266 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00194988 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00194988v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.title=Majoration%20du%20nombre%20de%20z%C3%A9ros%20d'une%20fonction%20m%C3%A9romorphe%20en%20dehors%20d'une%20droite%20verticale%20et%20applications&rft.atitle=Majoration%20du%20nombre%20de%20z%C3%A9ros%20d'une%20fonction%20m%C3%A9romorphe%20en%20dehors%20d'une%20droite%20verticale%20et%20applications&rft.au=VEL%C3%81SQUEZ%20CASTA%C3%91%C3%93N,%20Oswaldo&rft.genre=preprint |
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