Serre, Jean-Pierre Sur le nombre des points rationnels d’une courbe algébrique sur un corps fini. (French) Zbl 0538.14015 C. R. Acad. Sci., Paris, Sér. I 296, 397-402 (1983). The paper under review gives various ways to obtain upper or lower bounds for the number of rational points on a curve over a finite field, better than the Weil-estimates. Reviewer: G.Faltings Cited in 12 ReviewsCited in 82 Documents MSC: 14G05 Rational points 14G15 Finite ground fields in algebraic geometry 14H25 Arithmetic ground fields for curves 14N10 Enumerative problems (combinatorial problems) in algebraic geometry Keywords:zeta-functions; number of rational points; curve over a finite field; Weil-estimates × Cite Format Result Cite Review PDF Online Encyclopedia of Integer Sequences: Maximal number of rational points on a curve of genus 2 over GF(q), where q = A246655(n) is the n-th prime power > 1. Maximal number of rational points that a (smooth, geometrically irreducible) curve of genus 3 over the finite field GF(q) can have, where q is the n-th prime power >= 2. Maximal number of rational points on a curve of genus n over GF(2). Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 2 over the field F_2^n. Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 2 over the field F_3^n. Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 2 over the field F_5^n. ”Special” prime powers in Serre’s sense.