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Sziklai’s conjecture on the number of points of a plane curve over a finite field. III. (English) Zbl 1196.14030
Summary: We manage an upper bound for the number of rational points of a Frobenius nonclassical plane curve over a finite field. Together with previous results, the modified Sziklai conjecture is settled affirmatively.
For part II, cf. [Contemp. Math. 518, 225–234 (2010; Zbl 1211.14037)].

MSC:
14H50 Plane and space curves
14G15 Finite ground fields in algebraic geometry
14G05 Rational points
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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