144 citations · 741 across the 67 of their papers we have counts for
8 papers · 1 filter
A low-energy decomposition theorem
Antal Balog, Trevor D. Wooley
We prove that any finite set of real numbers can be split into two parts, one part being highly non-additive and the other highly non-multiplicative.
On the Waring--Goldbach problem for eighth and higher powers
Angel V. Kumchev, Trevor D. Wooley
Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for t…
Discrete Fourier restriction via efficient congruencing: basic principles
Trevor D. Wooley
We show that whenever , then for any complex sequence , one has $$\int_{[0,1)^k}\left| \sum_{|n|\le N}\mathfrak a_ne(α_1n+\ldots +α_kn^k…
Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations
Joerg Bruedern, Trevor D. Wooley
We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the a…
Additive representation in short intervals, II: sums of two like powers
Joerg Bruedern, Trevor D. Wooley
We establish that, for almost all natural numbers , there is a sum of two positive integral cubes lying in the interval . Here, the exponent lies half w…
Perturbations of Weyl sums
Trevor D. Wooley
Write . We show that there is a set of full measure with the property th…
Sums of three cubes, II
Trevor D. Wooley
Estimates are provided for th moments of cubic smooth Weyl sums, when , by enhancing the author's iterative method that delivers estimates beyond classical convexit…
Solvable points on smooth projective varieties
Trevor D. Wooley
We establish that smooth, geometrically integral projective varieties of small degree are not pointless in suitable solvable extensions of their field of definition, provided that…