On the Mertens Conjecture for Function Fields
Number Theory
2015-02-25 v2
Abstract
We study an analogue of the Mertens conjecture in the setting of global function fields. Building on the work of Cha, we show that most hyperelliptic curves do not satisfy the Mertens conjecture, but that if we modify the Mertens conjecture to have a larger constant, then this modified conjecture is satisfied by a positive proportion of hyperelliptic curves.
Cite
@article{arxiv.1210.0945,
title = {On the Mertens Conjecture for Function Fields},
author = {Peter Humphries},
journal= {arXiv preprint arXiv:1210.0945},
year = {2015}
}
Comments
17 pages. Several minor revisions and corrections based on referee comments. To appear in International Journal of Number Theory