On the distribution of the divisor function and Hecke eigenvalues
Number Theory
2016-01-12 v1
Abstract
We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by \'E. Fouvry, S. Ganguly, E. Kowalski, and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.
Keywords
Cite
@article{arxiv.1404.1579,
title = {On the distribution of the divisor function and Hecke eigenvalues},
author = {Stephen Lester and Nadav Yesha},
journal= {arXiv preprint arXiv:1404.1579},
year = {2016}
}
Comments
22 pages