Spectral symmetries of zeta functions
| dc.creator | Paugam, Frederic | |
| dc.date | 2008-03-03 | |
| dc.date | 2008-03-10 | |
| dc.date.accessioned | 2026-07-07T09:25:34Z | |
| dc.date.available | 2026-07-07T09:25:34Z | |
| dc.description | We define, answering a question of Sarnak in his letter to Bombieri, a symplectic pairing on the spectral interpretation (due to Connes and Meyer) of the zeroes of Riemann's zeta function. This pairing gives a purely spectral formulation of the proof of the functional equation due to Tate, Weil and Iwasawa, which, in the case of a curve over a finite field, corresponds to the usual geometric proof by the use of the Frobenius-equivariant Poincaré duality pairing in etale cohomology. We give another example of a similar construction in the case of the spectral interpretation of the zeroes of a cuspidal automorphic $L$-function, but this time of an orthogonal nature. These constructions are in adequation with Deninger's conjectural program and the arithmetic theory of random matrices. | |
| dc.description | 6 pages. Minor modification due to a problem with real zeroes of some general Dedekind zetas | |
| dc.identifier | https://arxiv.org/abs/0803.0199 | |
| dc.identifier | http://arxiv.org/abs/0803.0199 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156449 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11R42; 11F70 | |
| dc.title | Spectral symmetries of zeta functions | |
| dc.type | text |