Toroidal automorphic forms for some function fields
| dc.creator | Cornelissen, Gunther | |
| dc.creator | Lorscheid, Oliver | |
| dc.date | 2007-10-16 | |
| dc.date | 2008-03-27 | |
| dc.date.accessioned | 2026-07-07T09:28:35Z | |
| dc.date.available | 2026-07-07T09:28:35Z | |
| dc.description | Zagier introduced toroidal automorphic forms to study the zeros of zeta functions: an automorphic form on GL_2 is toroidal if all its right translates integrate to zero over all nonsplit tori in GL_2, and an Eisenstein series is toroidal if its weight is a zero of the zeta function of the corresponding field. We compute the space of such forms for the global function fields of class number one and genus g zero or one, and with a rational place. The space has dimension g and is spanned by the expected Eisenstein series. We deduce an "automorphic" proof for the Riemann hypothesis for the zeta function of those curves. | |
| dc.description | 7 pages, 2 figures; v2: minor corrections | |
| dc.identifier | https://arxiv.org/abs/0710.2994 | |
| dc.identifier | http://arxiv.org/abs/0710.2994 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157473 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11F12; 11G20; 14G10 | |
| dc.title | Toroidal automorphic forms for some function fields | |
| dc.type | text |