Improvements of The Weil Bound For Artin-Schreier Curves

2010/04/13 by Antonio Rojas‐León, Antonio Rojas-Leon, Daqing Wan +2
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1004.2224

revised version, title slightly changed, to appear in Math Ann

openalex publication_date 2010/04/13 · arxiv created 2010/12/04 · arxiv updated 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For Artin-Schreier curve y^q -y = f(x) defined over a finite field F_q of q elements, we show that the Weil bound for the number of the rational points over extension fields of F_q can often be greatly improved, essentially removing an extra factor of size about the square root of q in the error term.

Related

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• Artin-Schreier curves given by \mathbb F_q-linearized polynomials
• Refinements on higher order Weil-Oesterlé bounds via a Serre type argument