2 papers
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 expa…
math.NT2024
A nonabelian circle method
Nuno Arala, Jayce R. Getz, Jiaqi Hou +3
We count integral quaternion zeros of $γ_1^2 \pm \dots \pm γ_n^2$, giving an asymptotic when , and a likely near-optimal bound when . To do so, we introduce a new, n…