On the exceptional zeros of Rankin-Selberg L-functions

dc.creatorRamakrishnan, Dinakar
dc.creatorWang, Song
dc.date2001-08-08
dc.date.accessioned2026-07-07T04:42:54Z
dc.date.available2026-07-07T04:42:54Z
dc.descriptionThe 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.description31 pages. For ps, dvi and pdf formats of the paper, see http://www.math.caltech.edu/people/dinakar.html
dc.identifierhttps://arxiv.org/abs/math/0108054
dc.identifierhttp://arxiv.org/abs/math/0108054
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61988
dc.subjectNumber Theory
dc.subject11F70; 11F66; 11F55; 11F80
dc.titleOn the exceptional zeros of Rankin-Selberg L-functions
dc.typetext

Files

Collections