Majoration du nombre de zéros d'une fonction méromorphe en dehors d'une droite verticale et applications
| dc.creator | Castañón, Oswaldo Velásquez | |
| dc.date | 2007-12-08 | |
| dc.date.accessioned | 2026-07-07T08:48:06Z | |
| dc.date.available | 2026-07-07T08:48:06Z | |
| dc.description | 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.description | 46 pages; 2 figures | |
| dc.identifier | https://arxiv.org/abs/0712.1266 | |
| dc.identifier | http://arxiv.org/abs/0712.1266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143832 | |
| dc.subject | Number Theory | |
| dc.subject | Complex Variables | |
| dc.subject | 30C15, secondary 11M26 | |
| dc.title | Majoration du nombre de zéros d'une fonction méromorphe en dehors d'une droite verticale et applications | |
| dc.type | text |