## Nagoya Mathematical Journal

### On Waring’s problem: Three cubes and a minicube

#### Abstract

We establish that almost all natural numbers $n$ are the sum of four cubes of positive integers, one of which is no larger than $n^{5/36}$. The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.

#### Article information

Source
Nagoya Math. J., Volume 200 (2010), 59-91.

Dates
First available in Project Euclid: 28 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1293500427

Digital Object Identifier
doi:10.1215/00277630-2010-012

Mathematical Reviews number (MathSciNet)
MR2747878

Zentralblatt MATH identifier
1238.11090

#### Citation

Brüdern, Jörg; Wooley, Trevor D. On Waring’s problem: Three cubes and a minicube. Nagoya Math. J. 200 (2010), 59--91. doi:10.1215/00277630-2010-012. https://projecteuclid.org/euclid.nmj/1293500427

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