Li Coefficients for Automorphic L-Functions
| dc.creator | Lagarias, Jeffrey C. | |
| dc.date | 2004-04-21 | |
| dc.date | 2005-05-04 | |
| dc.date.accessioned | 2026-07-07T08:56:08Z | |
| dc.date.available | 2026-07-07T08:56:08Z | |
| dc.description | Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients lambda_n, indexed by the integers. We define similar coefficients attached to principal automorphic L-functions over GL(N). We relate these coefficients to values of Weil's quadratic functional for the associated automorphic representation, and deduce a Riemann hypothesis criterion in terms of positivity of the real parts of these coefficients. We determine asymptotics of the coefficients, both unconditionally and on the Riemann hypothesis, as n increases. We show the existence of an entire function of exponential type that interpolates the generalized Li coefficients at integer values. | |
| dc.description | 42 pages; minor corrections; references updated; correction to remainder term in Theorem 1.1 | |
| dc.identifier | https://arxiv.org/abs/math/0404394 | |
| dc.identifier | http://arxiv.org/abs/math/0404394 | |
| dc.identifier | Annales Institut Fourier 57 (2007), 1689-1740. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146502 | |
| dc.subject | Number Theory | |
| dc.subject | 11M26 22E55 | |
| dc.title | Li Coefficients for Automorphic L-Functions | |
| dc.type | text |