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The Quarterly Journal of Mathematics 2004 55(3):357-374; doi:10.1093/qmath/hah002
© 2004 by Oxford University Press
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On Roth's theorem concerning a cube and three cubes of primes

Xiumin Ren1 and Kai-Man Tsang1

1 Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong

In this paper, we prove that with at most O(N1271/1296+{varepsilon}) exceptions, all positive integers up to N are the sum of a cube and three cubes of primes. This improves an earlier result O(N169/170) of the first author and the classical result O(NL-A) of Roth.

Received 29 June 2003. Revised 28 November 2003.


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