144 citations · 741 across the 67 of their papers we have counts for
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Finite abelian groups via congruences
Trevor D. Wooley
For every finite abelian group , there are positive integers and such that is isomorphic to the multiplicative group of -th powers of reduced residues modulo .
The paucity problem for certain symmetric Diophantine equations
Trevor D. Wooley
Let be integral linear combinations of elementary symmetric polynomials with , where $1\le k_1<k…
Pairs of diagonal quartic forms: the asymptotic formulae
Joerg Bruedern, Trevor D. Wooley
We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in or more variables. In certain cases, pairs…
Partitio Numerorum: sums of a prime and a number of -th powers
Joerg Bruedern, Trevor D. Wooley
Let be a natural number and let be the unique real solution of the equation in . Then, when , we establish an asymp…
On Waring's problem for larger powers
Joerg Bruedern, Trevor D. Wooley
Let denote the least number having the property that every sufficiently large natural number is the sum of at most positive integral -th powers. Then for all $k\i…
Subconvexity in inhomogeneous Vinogradov systems
Trevor D. Wooley
When and are natural numbers and , denote by the number of integral solutions of the system \[ \sum_{i=1}^s(x_i^j-y_i^j)=h_…
Subconvexity in the inhomogeneous cubic Vinogradov system
Trevor D. Wooley
When , denote by the number of integral solutions to the system \[ \sum_{i=1}^6(x_i^j-y_i^j)=h_j\quad (1\le j\le 3), \] with $1\le x_i,y_…
Subconvexity and the Hilbert-Kamke Problem
Trevor D. Wooley
When and are large natural numbers, denote by the number of solutions in non-negative integers to the system \[ x_1…