Riemann's Zeta Function and Beyond
| dc.creator | Gelbart, Stephen S. | |
| dc.creator | Miller, Stephen D. | |
| dc.date | 2003-09-30 | |
| dc.date.accessioned | 2026-07-07T05:01:33Z | |
| dc.date.available | 2026-07-07T05:01:33Z | |
| dc.description | In recent years L-functions and their analytic properties have assumed a central role in number theory and automorphic forms. In this expository article, we describe the two major methods for proving the analytic continuation and functional equations of $L$-functions: the method of integral representations, and the method of Fourier expansions of Eisenstein series. Special attention is paid to technical properties, such as boundedness in vertical strips; these are essential in applying the converse theorem, a powerful tool that uses analytic properties of L-functions to establish cases of Langlands functoriality conjectures. We conclude by describing striking recent results which rest upon the analytic properties of L-functions. | |
| dc.description | Survey, 63 pages, to appear in the Bulletin of the A.M.S., 2004 | |
| dc.identifier | https://arxiv.org/abs/math/0309478 | |
| dc.identifier | http://arxiv.org/abs/math/0309478 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68711 | |
| dc.subject | Number Theory | |
| dc.subject | Complex Variables | |
| dc.title | Riemann's Zeta Function and Beyond | |
| dc.type | text |