ON THE MERTENS CONJECTURE FOR FUNCTION FIELDS

被引：3

作者：

Humphries, Peter ^{[1
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2014年 / 10卷 / 02期

关键词：

Mertens conjecture; function field; Mobius function; hyperelliptic curve;

D O I：

10.1142/S1793042113500978

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：341 / 361

页数：21

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