Nuno Arala

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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.NT2023

The analytic Hasse Principle for certain singular intersections of quadrics in $P^{9}$

Nuno Arala

For a pair of quadratic forms with rational coefficients in at least $10$ variables, we prove an asymptotic formula for the number of common zeros under the assumption that the two…

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…

A nonabelian circle method

The analytic Hasse Principle for certain singular intersections of quadrics in P9

Lines of polynomials with alternating Galois group

The analytic Hasse Principle for certain singular intersections of quadrics in $P^{9}$