# Sums of Three Cubes

@article{Vaughan1985SumsOT,
title={Sums of Three Cubes},
author={R. C. Vaughan},
journal={Bulletin of The London Mathematical Society},
year={1985},
volume={17},
pages={17-20}
}
• R. Vaughan
• Published 1985
• Mathematics
• Bulletin of The London Mathematical Society
On the Waring–Goldbach problem for one square and five cubes
• Mathematics
International Journal of Number Theory
• 2018
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
• Mathematics
Acta Arithmetica
• 2020
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
• Mathematics
• 2017
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
• Mathematics
• 2002
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
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• Mathematics
Acta Arithmetica
• 2022
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.
AN OBSERVATION CONCERNING THE REPRESENTATION OF POSITIVE INTEGERS AS A SUM OF THREE CUBES
• Mathematics
• 2021
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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