A bound on the number of points of a curve in projective space over a finite field

2011/08/25 by Masaaki Homma, Homma, Masaaki · 1 citation
Computer Science · Mathematics · #11G20 #14G15 #14H25 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1108.4975

openalex publication_date 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a nondegenerate irreducible curve C of degree d in \Bbb P^r over \Bbb F_q with r ≥ 3, we prove that the number N_q(C) of \Bbb F_q-points of C satisfies the inequality N_q(C) ≤ (d-1)q +1, which is known as Sziklai's bound if r=2.

Cited by

• On the constant D(q) defined by Homma

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