Moscow Mathematical Journal

Volume 15, Issue 4, October–December 2015 pp. 615–627.

On the Maximum Number of Rational Points on Singular Curves over Finite Fields

Authors: Yves Aubry (1) and Annamaria Iezzi (2)
Author institution:(1) Institut de Mathématiques de Toulon, Université de Toulon, France and Institut de Mathématiques de Marseille, CNRS-UMR 7373, Aix-Marseille Université, France
(2) Institut de Mathématiques de Marseille, CNRS-UMR 7373, Aix-Marseille Université, France

Summary:

We give a construction of singular curves with many rational points over finite fields. This construction enables us to prove some results on the maximum number of rational points on an absolutely irreducible projective algebraic curve defined over 𝔽_q of geometric genus g and arithmetic genus π.

2010 Math. Subj. Class. 14H20, 11G20, 14G15.

Keywords: Singular curves, finite fields, rational points, zeta function.

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