144 citations · 741 across the 67 of their papers we have counts for
8 papers · 1 filter
Equidistribution of polynomial sequences in function fields, with applications
Thái Hoàng Lê, Yu-Ru Liu, Trevor D. Wooley
We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greate…
Multigrade efficient congruencing and Vinogradov's mean value theorem
Trevor D. Wooley
We develop a multigrade enhancement of the efficient congruencing method to estimate Vinogradov's integral of degree for moments of order , thereby obtaining near-optimal e…
The asymptotic formula in Waring's problem: higher order expansions
Robert C. Vaughan, Trevor D. Wooley
When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum o…
Artin's Conjecture and systems of diagonal equations
Trevor D. Wooley
We show that Artin's conjecture concerning p-adic solubility of Diophantine equations fails for infinitely many systems of r homogeneous diagonal equations whenever r>1.
Cubic moments of Fourier coefficients and pairs of diagonal quartic forms
Joerg Bruedern, Trevor D. Wooley
We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensi…
On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing
Kevin Ford, Trevor D. Wooley
We enhance the efficient congruencing method for estimating Vinogradov's integral for moments of order , with . In this way, we prove the main conjecture for s…
The Hasse principle for systems of diagonal cubic forms
Joerg Bruedern, Trevor D. Wooley
We establish the Hasse Principle for systems of r simultaneous diagonal cubic equations whenever the number of variables exceeds 6r and the associated coefficient matrix contains n…
On Linnik's conjecture: sums of squares and microsquares
Trevor D. Wooley
We show that almost all natural numbers n not divisible by 4, and not congruent to 7 modulo 8, are represented as the sum of three squares, one of which is the square of an integer…