Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem

Details Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem

2010-04-15

arxiv.org/abs/1004.2670v1

Mathematics

Number Theory

Scientific paper

We apply a method of Davenport to improve several estimates for slim
exceptional sets associated with the asymptotic formula in Waring's problem. In
particular, we show that the anticipated asymptotic formula in Waring's problem
for sums of seven cubes holds for all but $O(N^{1/3+\epsilon})$ of the natural
numbers not exceeding $N$.

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