On the constant D(q) defined by Homma

2022/01/03 by Peter Beelen, Beelen, Peter, Maria Montanucci +3
Computer Science · Mathematics · #11G20 #14G15 #14H25 #14H50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.00602

openalex publication_date 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a projective, irreducible, nonsingular algebraic curve over the finite field \mathbbF_q with q elements and let |X(\mathbbF_q)| and g(\mathcal X) be its number of rational points and genus respectively. The Ihara constant A(q) has been intensively studied during the last decades, and it is defined as the limit superior of |X(\mathbbF_q)|/g(\mathcal X) as the genus of \mathcal X goes to infinity. In 2012 Homma defined an analogue D(q) of A(q), where the nonsingularity of \mathcal X is dropped and g(\mathcal X) is replaced with the degree of \mathcal X. We will call D(q) Homma's constant. In this paper, upper and lower bounds for the value of D(q) are found.

Citations

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

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