This article is cited in 3 papers

On the maximum number of rational points on singular curves over finite fields

Yves Aubry^ab, Annamaria Iezzi<sup>a

a</sup> Institut de Mathématiques de Marseille, CNRS-UMR 7373, Aix-Marseille Université, France
^b Institut de Mathématiques de Toulon, Université de Toulon, France

Abstract: 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 $\mathbb F_q$ of geometric genus $g$ and arithmetic genus $\pi$.

Key words and phrases: singular curves, finite fields, rational points, zeta function.

MSC: 14H20, 11G20, 14G15

Received: January 15, 2015; in revised form August 17, 2015

Language: English

DOI: 10.17323/1609-4514-2015-15-4-615-627

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