%L discovery1569442
%D 2014
%P 341-361
%O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
%T On the Mertens Conjecture for Function Fields
%X We study the natural 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.
%K Mertens Conjecture; Function Field; Möbius Function; Hyperelliptic Curve
%V 10
%A Peter Humphries
%J International Journal of Number Theory
%N 02