Families of L-functions and their Symmetry
Number Theory
2015-09-17 v2
Abstract
In [90] the first-named author gave a working definition of a family of automorphic L-functions. Since then there have been a number of works [33], [107], [67] [47], [66] and especially [98] by the second and third-named authors which make it possible to give a conjectural answer for the symmetry type of a family and in particular the universality class predicted in [64] for the distribution of the zeros near s=1/2. In this note we carry this out after introducing some basic invariants associated to a family.
Cite
@article{arxiv.1401.5507,
title = {Families of L-functions and their Symmetry},
author = {Peter Sarnak and Sug-Woo Shin and Nicolas Templier},
journal= {arXiv preprint arXiv:1401.5507},
year = {2015}
}