| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4582912 | Finite Fields and Their Applications | 2013 | 8 Pages |
Abstract
In this paper we consider the question of whether there exists a hyperelliptic curve of genus g which is defined over Fq but has no rational points over Fq for various pairs (g,q). 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 Fp of every genus g⩾q−1.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
