Incidences of Cubic Curves in Finite Fields

TL;DR

This paper establishes an incidence bound between points and cubic curves over prime fields, extending previous methods to this specific algebraic setting.

Contribution

It introduces a generalized approach for incidence bounds applicable to cubic curves over finite fields, building on prior work with new algebraic techniques.

Findings

Proved a new incidence bound for points and cubic curves over prime fields.

Extended existing methods to handle cubic curves specifically.

Provides a foundation for further research in finite field incidence geometry.

Abstract

In this paper we prove an incidence bound for points and cubic curves over prime fields. The methods generalise those used by Mohammadi, Pham, and Warren (2021).