To develop a higher-degree analogy of the Szemerédi–Trotter theorem in the context of finite fields and polynomial expansion.
Utilized spectral theory methods for the analysis.
Applied concepts from algebraic geometry in findings.
Focused on establishing relationships in finite fields.
Confirmed the existence of a higher-degree Szemerédi–Trotter-type theorem.
Illustrated the application of this theorem in polynomial expansion scenarios.
Abstract
We use spectral theory and algebraic geometry to establish a higher-degree analogue of a Szemerédi–Trotter-type theorem over finite fields, with an application to polynomial expansion.