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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On certain maximal hyperelliptic curves related to Chebyshev polynomials

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Author(s):
Tafazolian, Saeed [1] ; Top, Jaap [2]
Total Authors: 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
Total Affiliations: 2
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