Sziklai's conjecture on the number of points of a plane curve over a finite field II

TL;DR

This paper confirms Sziklai's conjecture regarding the maximum number of points on a nonsingular plane curve over a finite field, providing a definitive answer to an open problem in finite geometry.

Contribution

It proves Sziklai's conjecture for nonsingular plane curves over finite fields, advancing understanding in finite geometry and algebraic curves.

Findings

Confirmed Sziklai's conjecture for nonsingular curves

Established bounds on the number of points on such curves

Enhanced theoretical understanding of finite field curves

Abstract

We settle the conjecture posed by Sziklai on the number of points of a plane curve over a finite field under the assumption that the curve is nonsingular.