Nuno Arala

collaborators

3 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 expan…

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 $n \geq 9$ , and a likely near-optimal bound when $n = 8$ . To do so, we introduce a new, non…

math.NT2022

Lines of polynomials with alternating Galois group

Nuno Arala

We study the problem of existence of one-parameter, linear families of polynomials of degree n all of whose polynomials have Galois group A_n. The methods we use have a strong geom…