On certain maximal hyperelliptic curves related to Chebyshev polynomials
Saeed Tafazolian, Top, Jakob; id_orcid 0000-0002-5265-7608 · University of Groningen research database (University of Groningen / Centre for Information Technology) · 2019
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 C over a finite field Fq given by y2=φd(x) is maximal over the finite field Fq of cardinality q2. Here φd(x) denotes the Chebyshev polynomial of degree d. The same question is studied for the curves given by y2=(x±2)φd(x), and also for y2=(x2−4)φd(x). Our results generalize some of the statements in [12].