6 citations · 9 across the 21 of their papers we have counts for
26 papers · 1 filter
Structure and paucity in affine diagonal systems, I
Julia Brandes, Trevor D. Wooley
Let and . We show that whenever 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 …
Strong paucity in the Brüdern-Robert Diophantine system
Trevor D. Wooley
Let be a natural number with , and let . We consider the number of integral solutions of the system of simultaneous Diophantine equations \[ x…
Subconvex -sets, Weyl's inequality, and equidistribution
Trevor D. Wooley
We examine sets of natural numbers having the property that for some real number , one has the subconvex bound $$\int_0^1 \Bigl| \sum_{n\in \mathscr A\cap…
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 . In particular, when and…
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…
Partitio Numerorum: sums of squares and higher powers
Joerg Bruedern, Trevor D. Wooley
We survey the potential for progress in additive number theory arising from recent advances concerning major arc bounds associated with mean value estimates for smooth Weyl sums. W…