1 citations · 2 across the 7 of their papers we have counts for
7 papers
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…
A nonabelian circle method
Nuno Arala, Jayce R. Getz, Jiaqi Hou +3
We count integral quaternion zeros of , giving an asymptotic when , and a likely near-optimal bound when . To do so, we introduce a new, non…
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,…
The analytic Hasse Principle for certain singular intersections of quadrics in
Nuno Arala
For a pair of quadratic forms with rational coefficients in at least variables, we prove an asymptotic formula for the number of common zeros under the assumption that the two…
A maximal extension of the Bloom-Maynard bound for sets with no square differences
Nuno Arala
We show that if is a polynomial of degree such that the congruence has a solution for every positive integer , then any subset of $…
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…
On the density of a set of primes associated to an Elliptic Curve
Nuno Arala
For a given elliptic curve defined over the rationals, we study the density of primes satisfying and give a conjectural value for th…