Document Type

Article

Publication Date

2013

Department

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.

Comments

Ryan P. Becker: Class of 2013

Required Publisher's Statement

Original version available from the publisher at: http://www.sciencedirect.com/science/article/pii/S1071579713000166

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