Low-lying zeros of Dirichlet L-functions

Details Low-lying zeros of Dirichlet L-functions Low-lying zeros of Dirichlet L-functions

2011-11-16

arxiv.org/abs/1111.3896v1

Mathematics

Number Theory

Version 1.0, 30 pages

Scientific paper

We study the distribution of the zeros near the central point for weighted and unweighted families of Dirichlet L-functions. As the conductors tend to infinity, the main term of the 1-level densities agrees with the scaling limit of unitary matrices for even C^2 test functions whose Fourier transforms are supported in (-2,2), supporting the Katz-Sarnak conjecture. The lower order terms agree with the prediction from the L-function Ratios Conjecture in the regime where both can be computed, though we are able to compute beyond square-root cancelation, thus going further than what the Ratios Conjecture can predict. We also investigate the consequences of conjectures about the modulus dependence in the error terms in the distribution of primes in residue classes. We show how some natural conjectures imply that the 1-level densities agree with unitary matrices for arbitrary support, while some weaker conjectures still give an improvement over (-2,2), allowing support up to (-4,4).

Affiliated with

Also associated with

No associations

Rating

Low-lying zeros of Dirichlet 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 Low-lying zeros of Dirichlet L-functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Low-lying zeros of Dirichlet L-functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69034