On the exceptional zeros of Rankin-Selberg L-functions
| dc.creator | Ramakrishnan, Dinakar | |
| dc.creator | Wang, Song | |
| dc.date | 2001-08-08 | |
| dc.date.accessioned | 2026-07-07T04:42:54Z | |
| dc.date.available | 2026-07-07T04:42:54Z | |
| dc.description | The main objects of study in this article are two classes of Rankin-Selberg L-unctions, namely L(s, f \times g) and L(s, sym^2(g) \times sym^2(g)), where f, g are newforms, holomorphic or of Maass type, on the upper half plane, and sym^2(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any Landau-Siegel zeros. These zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound on the norm of sym^2(g). | |
| dc.description | 31 pages. For ps, dvi and pdf formats of the paper, see http://www.math.caltech.edu/people/dinakar.html | |
| dc.identifier | https://arxiv.org/abs/math/0108054 | |
| dc.identifier | http://arxiv.org/abs/math/0108054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61988 | |
| dc.subject | Number Theory | |
| dc.subject | 11F70; 11F66; 11F55; 11F80 | |
| dc.title | On the exceptional zeros of Rankin-Selberg L-functions | |
| dc.type | text |