T. Wooley

activity

20032026

most citedThe cubic case of the main conjecture in Vinogradov's mean value theorem

144 citations · 741 across the 67 of their papers we have counts for

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math.NT2026

Sharp mean value estimates in the absence of translation-dilation invariance

Trevor D. Wooley

We establish sharp mean value estimates for various exponential sums lacking translation-dilation invariance properties. For example, suppose that $k \geq 1$ and $s > 0$ . Then, for eac…

math.NT2026

The main conjecture for a Vinogradov subsystem

Trevor D. Wooley

When $k \geq 2$ and $s > 0$ , we establish that for each $ε > 0$ , one has \[ \int_{[0,1)^{k-1}}\biggl| \sum_{1\le x\le X}e(α_2x^2+\ldots +α_k x^k)\biggr|^{2s}\,{\rm d}\boldsymbo…

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 Brüdern-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…