Document Type
Article
Publication Date
2013
Department 1
Mathematics
Abstract
In this paper we consider the question of whether there exists a hyperelliptic curve of genus g which is defined over but has no rational points over for various pairs . As an example of such a result, we show that if p is a prime such that is also prime then there will be pointless hyperelliptic curves over of every genus.
Copyright Note
This is the author's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
DOI
10.1016/j.ffa.2013.01.008
Recommended Citation
Becker, Ryan and Darren Glass. “Pointless Hyperelliptic Curves.” Finite Fields and Their Applications 21 (2013): 50-57.
Required Publisher's Statement
Original version available from the publisher at: http://www.sciencedirect.com/science/article/pii/S1071579713000166
Comments
Ryan P. Becker: Class of 2013