Additive representation in thin sequences, I: Waring's problem for cubes

Abstract

In this paper we investigate representation of numbers from certain thin sequences like the squares or cubes by sums of cubes. It is shown, in particular, that almost all values of an integral cubic polynomial are sums of six cubes. The methods are very flexible and may be applied to many related problems. (C) 2001 Editions scientifiques et medicales Elsevier SAS.