A note on some Picard curves over finite fields

Author(s)

Kazemifard, Ahmad ^[1] ; Tafazolian, Saeed ^[2]

Affiliation

^[1] Shahid Chamran Univ, Dept Math, Ahwaz - Iran

^[2] Univ Estadual Campinas, UNICAMP, Inst Math Stat & Comp Sci IMECC, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: FINITE FIELDS AND THEIR APPLICATIONS; v. 34, p. 107-122, JUL 2015.
• Web of Science Citations: 0

Abstract

In this note we provide a complete classification for the Newton polygon of the Picard curves y(3) = x(4) - x and y(3) = x(4) - 1 defined over a finite field of characteristic p > 3. In fact, we complete the results obtained in {[}19]. Using these results, we determine all finite fields over which these curves attain the Hasse-Weil upper bound. (C) 2014 Published by Elsevier Inc. (AU)

• FAPESP's process: 12/02255-3 - CURVES OVER FINITE FIELDS
• Grantee: Saeed Tafazolian
• Support Opportunities: Scholarships in Brazil - Post-Doctoral