Rational points on certain hyperelliptic curves over finite fields
| dc.creator | Ulas, Maciej | |
| dc.date | 2007-06-11 | |
| dc.date.accessioned | 2026-07-07T08:04:54Z | |
| dc.date.available | 2026-07-07T08:04:54Z | |
| dc.description | Let $K$ be a field, $a, b\in K$ and $ab\neq 0$. Let us consider the polynomials $g_{1}(x)=x^n+ax+b, g_{2}(x)=x^n+ax^2+bx$, where $n$ is a fixed positive integer. In this paper we show that for each $k\geq 2$ the hypersurface given by the equation \begin{equation*} S_{k}^{i}: u^2=\prod_{j=1}^{k}g_{i}(x_{j}),\quad i=1, 2. \end{equation*} contains a rational curve. Using the above and Woestijne's recent results \cite{Woe} we show how one can construct a rational point different from the point at infinity on the curves $C_{i}:y^2=g_{i}(x), (i=1, 2)$ defined over a finite field, in polynomial time. | |
| dc.description | Revised version will appear in Bull. Polish Acad. Sci. Math | |
| dc.identifier | https://arxiv.org/abs/0706.1448 | |
| dc.identifier | http://arxiv.org/abs/0706.1448 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130134 | |
| dc.subject | Number Theory | |
| dc.subject | 11D25; 11D41; 14G15 | |
| dc.title | Rational points on certain hyperelliptic curves over finite fields | |
| dc.type | text |