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math.CO2024
Incidence geometry and polynomial expansion over finite fields
Nuno Arala, Sam Chow
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 expan…
math.CO2024
Expansion properties of polynomials over finite fields
Nuno Arala, Sam Chow
We establish expansion properties for suitably generic polynomials of degree in variables over finite fields. In particular, we show that if $P\in\mathbb{F}_q[x_1,\ldots,…