144 citations · 741 across the 67 of their papers we have counts for
7 papers · 1 filter
On Sums of Powers of Almost Equal Primes
Bin Wei, Trevor D. Wooley
We investigate the Waring-Goldbach problem of representing a positive integer as the sum of th powers of almost equal prime numbers. Define when ,…
Rational solutions of pairs of diagonal equations, one cubic and one quadratic
Trevor D. Wooley
We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument . Subject to modest local solubility hypotheses, we thereby…
Translation invariance, exponential sums, and Waring's problem
Trevor D. Wooley
We describe mean value estimates for exponential sums of degree exceeding 2 that approach those conjectured to be best possible. The vehicle for this recent progress is the efficie…
Correlation estimates for sums of three cubes
Joerg Bruedern, Trevor D. Wooley
We establish estimates for linear correlation sums involving sums of three positive integral cubes. Under appropriate conditions, the underlying methods permit us to establish the…
Mean value estimates for odd cubic Weyl sums
Trevor D. Wooley
We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument . The first substantial advance in this topic for over 60 years, t…
The cubic case of the main conjecture in Vinogradov's mean value theorem
Trevor D. Wooley
We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov's integral of degree for moments of order , establishing strongly diagonal behavio…
Approximating the main conjecture in Vinogradov's mean value theorem
Trevor D. Wooley
We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree for moments of order , establishing strongly diagonal behaviour for $1\le s\le \frac{…