Central limit theorem for Artin $L$-functions
Number Theory
2015-06-25 v1
Abstract
We show that the sum of the traces of Frobenius elements of Artin -functions in a family of -fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for and -fields. We also show central limit theorem for modular form -functions with the trivial central character with respect to congruence subgroups as the level goes to infinity.
Cite
@article{arxiv.1506.07416,
title = {Central limit theorem for Artin $L$-functions},
author = {Peter J. Cho and Henry H. Kim},
journal= {arXiv preprint arXiv:1506.07416},
year = {2015}
}