A special case of Vinogradov's mean value theorem
The representation of almost all numbers as sums of unlike powers
We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.
On sums of two cubes: an Ω₊-estimate for the error term
The arithmetic function counts the number of ways to write a natural number n as a sum of two kth powers (k ≥ 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of leads in a natural way to a certain error term which is known to be in mean-square. In this article it is proved that as t → ∞. Furthermore, it is shown that a similar result would be true for every fixed k > 3 provided that a certain set of algebraic numbers contains a sufficiently...
Additive representation in thin sequences, III: asymptotic formulae
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