On the exceptional zeros of Rankin-Selberg L-functions

Details On the exceptional zeros of Rankin-Selberg L-functions On the exceptional zeros of Rankin-Selberg L-functions

2001-08-08

arxiv.org/abs/math/0108054v1

Mathematics

Number Theory

31 pages. For ps, dvi and pdf formats of the paper, see http://www.math.caltech.edu/people/dinakar.html

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

On the exceptional zeros of Rankin-Selberg L-functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the exceptional zeros of Rankin-Selberg L-functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the exceptional zeros of Rankin-Selberg L-functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-682135