Sums of Three Cubes

  title={Sums of Three Cubes},
  author={R. C. Vaughan},
  journal={Bulletin of The London Mathematical Society},
  • R. Vaughan
  • Published 1985
  • Mathematics
  • Bulletin of The London Mathematical Society
On the Waring–Goldbach problem for one square and five cubes
Let [Formula: see text] denote an almost-prime with at most [Formula: see text] prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even
Sums of cubes with shifts
  • Sam Chow
  • Mathematics
    J. Lond. Math. Soc.
  • 2015
It is shown that if $\eta$ is real, $\tau >0$ is sufficiently large, and $s \ge 9$, then there exist integers $x_1 > \mu_1, \ldots, x_s > \Mu_s$ such that $|F(\mathbf{x})- \tau| < \eta$.
(2015). Sums of cubes with shifts. Journal of the London Mathematical Society , 91 (2), 343-366.
  • Mathematics
  • 2014
. Let µ 1 , . . . , µ s be real numbers, with µ 1 irrational. We investigate sums of shifted cubes F ( x 1 , . . . , x s ) = ( x 1 − µ 1 ) 3 + . . . + ( x s − µ s ) 3 . We show that if η is real, τ >
The density of integers representable as the sum of four prime cubes
The set of integers which can be written as the sum of four prime cubes has lower density at least $0.009664$. This improves earlier bounds of $0.003125$ by Ren and $0.005776$ by Liu.
Waring-Goldbach Problem: One Square, Four Cubes and Higher Powers
Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that, for $12\leqslant b\leqslant 35$ and for every
Waring's problem: A survey
It is presumed that by this, in modern notation, Waring meant that for every k ≥ 3 there are numbers s such that every natural number is the sum of at most s k-th powers of natural numbers and that
The use in additive number theory of numbers without large prime factors
  • R. Vaughan
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences
  • 1993
In the past few years considerable progress has been made with regard to the known upper bounds for G(k) in Waring’s problem, that is, the smallest s such that every sufficiently large natural number
On smooth Weyl sums over biquadrates and Waring’s problem
We provide estimates for s moments of biquadratic smooth Weyl sums, when 10 6 s 6 12, by enhancing the second author’s iterative method that delivers estimates beyond the classical convexity barrier.
In recent years there has been significant progress on the problem of representing integers as a sum of three cubes. Most significantly are the relatively new solutions found by Booker and Sutherland
Exceptional Sets for Sums of Prime Cubes in Short Interval
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