On Roth's theorem concerning a cube and three cubes of primes

Authors: Ren, Xiumin; Tsang, Kai-Man

Source: Quarterly Journal of Mathematics, Volume 55, Number 3, September 2004 , pp. 357-374(18)

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Abstract:

In this paper, we prove that with at most O(N^1271/1296+ɛ) exceptions, all positive integers up to N are the sum of a cube and three cubes of primes. This improves an earlier result O(N^169/170) of the first author and the classical result O(NL^-A) of Roth.

Document Type: Research article

Publication date: 2004-09-01

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.