T. Wooley

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math.NT2026

Structure and paucity in affine diagonal systems, I

Julia Brandes, Trevor D. Wooley

Let $ε > 0$ and $h \in Z^{3}$ . We show that whenever $P$ is large and the system \[ x_1^j+x_2^j-y_1^j-y_2^j=h_j\quad (j=1,2,3) \] has more than $P^{ε}$ …

math.NT2026

Strong paucity in the BrÃ¼dern-Robert Diophantine system

Trevor D. Wooley

Let $k$ be a natural number with $k \geq 2$ , and let $ε > 0$ . We consider the number $V_{k}^{*} (P)$ of integral solutions of the system of simultaneous Diophantine equations \[ x…

math.NT2025

Subconvex $L^{p}$ -sets, Weyl's inequality, and equidistribution

Trevor D. Wooley

We examine sets $A$ of natural numbers having the property that for some real number $p \in (0, 2)$ , one has the subconvex bound $$\int_0^1 \Bigl| \sum_{n\in \mathscr A\cap…

math.NT2024

On $2$ -superirreducible polynomials over finite fields

Jonathan W. Bober, Lara Du, Dan Fretwell +2

We investigate $k$ -superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most $k$ .…

math.NT2024

Estimates for smooth Weyl sums on minor arcs

Joerg Bruedern, Trevor D. Wooley

We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of $I^\pm n^{k}$ . In particular, when $k \geq 6$ and…

math.NT2024

Estimates for smooth Weyl sums on major arcs

Joerg Bruedern, Trevor D. Wooley

We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy-Littlewood method. In particular, we derive mean value estimates on major arcs f…

Structure and paucity in affine diagonal systems, I

Strong paucity in the BrÃ¼dern-Robert Diophantine system

Subconvex Lp-sets, Weyl's inequality, and equidistribution

On 2-superirreducible polynomials over finite fields

Estimates for smooth Weyl sums on minor arcs

Estimates for smooth Weyl sums on major arcs

Subconvex $L^{p}$ -sets, Weyl's inequality, and equidistribution

On $2$ -superirreducible polynomials over finite fields