Pointless hyperelliptic curves

被引：2
|
作者：
Becker, Ryan [1 ]
Glass, Darren [1 ]
机构：
[1] Gettysburg Coll, Dept Math, Gettysburg, PA 17325 USA
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 21卷
基金：
美国安德鲁·梅隆基金会;
关键词：
Hyperelliptic curves; Finite fields; RATIONAL-POINTS; FINITE-FIELDS; NUMBER;
D O I：
10.1016/j.ffa.2013.01.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider. the question of whether there exists a hyperelliptic curve of genus g which is defined over F-q but has no rational points over F-q for various pairs (g, q). As an example of such a result, we show that if p is a prime such that q = p-1/2 is also prime then there will be pointless hyperelliptic curves over F-p of every genus g >= q - 1. (C) 2013 Elsevier Inc. All rights reserved.
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页码：50 / 57
页数：8
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