Zeta functions of trinomial curves and maximal curves

2014/08/10 by Menglong Nie, Nie, Menglong · 1 citation
Computer Science · Mathematics · #11G20 #14H45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G20 #msc:14H45

paper · pdf · doi:10.48550/arxiv.1408.2178

37 pages

arxiv created 2014/08/10 · openalex publication_date 2014/08/10 · arxiv updated 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the zeta functions of trinomial curves in terms of Gauss sums and Jacobi sums, and we obtain an explicit formula of the genus of a trinomial curve over a finite field, then we study the conditions for a trinomial curve to be a maximal curve over a finite field.

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• Minimal value set binomials and Frobenius nonclassical curves

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