A Polya-Hilbert operator for automorphic L-functions
| dc.creator | Deitmar, Anton | |
| dc.date | 1999-03-11 | |
| dc.date | 1999-03-17 | |
| dc.date.accessioned | 2026-07-07T05:28:17Z | |
| dc.date.available | 2026-07-07T05:28:17Z | |
| dc.description | We generalize the first part of A. Connes paper (math/9811068) on the zeroes of the Riemann zeta function from a number field $k$ to any simple algebra $M$ over $k$. To a given automorphic representation $π$ of the reductive group $M^\times$ of invertible elements of $M$ we find a Hilbert space $H_π$ and an operator $D_π$ (Polya-Hilbert operator), which is the infinitesimal generator of a canonical flow such that the spectrum of $D_π$ coincides with the purely imaginary zeroes of the function $L(π,\rez{2} +z)$. As a byproduct we get holomorphicity of all automorphic $L$-functions, not only the cuspidal ones. | |
| dc.description | LATEX, 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/9903061 | |
| dc.identifier | http://arxiv.org/abs/math/9903061 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78203 | |
| dc.subject | Number Theory | |
| dc.title | A Polya-Hilbert operator for automorphic L-functions | |
| dc.type | text |