On certain maximal hyperelliptic curves related to Chebyshev polynomials

Author(s)

Tafazolian, Saeed ^[1] ; Top, Jaap ^[2]

Affiliation

^[1] Univ Campinas UNICAMP, Inst Math Stat & Comp Sci IMECC, Rua Sergio Buarque de Holanda 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil

^[2] Johan Bernoulli Inst Math & Comp Sci, Nijenborgh 9, NL-9747 AG Groningen - Netherlands

• Document type: Journal article
• Source: JOURNAL OF NUMBER THEORY; v. 203, p. 276-293, OCT 2019.
• Web of Science Citations: 0

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 C over a finite field F-q2 given by y(2) = phi(d)(x) is maximal over the finite field F-q2 of cardinality q(2). Here phi(d)(x) denotes the Chebyshev polynomial of degree d. The same question is studied for the curves given by y(2) = (x +/- 2)phi(d)(x), and also for y(2) = (x(2) - 4)phi(d)(x). Our results generalize some of the statements in {[}12]. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 17/19190-5 - Curves with many rational points over finite fields and their applications in coding theory
• Grantee: Saeed Tafazolian
• Support Opportunities: Regular Research Grants