Photo by berlinboudoir from unsplash
We study hyperelliptic curves arising from Chebyshev polynomials. The aim of this paper is to characterize the pairs $(q,d)$ such that the hyperelliptic curve $\cC$ over a finite field $\FF_{q^2}$… Click to show full abstract
We study hyperelliptic curves arising from Chebyshev polynomials. The aim of this paper is to characterize the pairs $(q,d)$ such that the hyperelliptic curve $\cC$ over a finite field $\FF_{q^2}$ corresponding to the equation $y^2 = \varphi_{d}(x)$ is maximal over the finite field $\FF_{q^2}$ of cardinality $q^2$. Here $\varphi_{d}(x)$ denotes the Chebyshev polynomial of degree $d$. The same question is studied for the curves corresponding to $y^2=(x\pm 2) \varphi_{d}(x)$, and also for $y^2=(x^2-4)\varphi_d(x)$.
Keywords:
hyperelliptic curves;
curves related;
related chebyshev;
maximal hyperelliptic;
chebyshev polynomials;
certain maximal
Journal Title: Journal of Number Theory
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Journal of Number Theory
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!