Nuno Arala

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20212024

most citedA maximal extension of the Bloom-Maynard bound for sets with no square differences

1 citations · 2 across the 7 of their papers we have counts for

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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.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.CO2024

Expansion properties of polynomials over finite fields

Nuno Arala, Sam Chow

We establish expansion properties for suitably generic polynomials of degree $d$ in $d + 1$ variables over finite fields. In particular, we show that if $P\in\mathbb{F}_q[x_1,\ldots,…