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

Abstract

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 $N$.

Cited by in corpus (5)

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• Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations
• Correlation estimates for sums of three cubes
• Cubic moments of Fourier coefficients and pairs of diagonal quartic forms
• Exceptional sets for Diophantine inequalities