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Article Dans Une Revue Acta Arithmetica Année : 2016

Weyl sums, mean value estimates, and Waring's problem with friable numbers

Résumé

In this paper we study Weyl sums over friable integers (more precisely $y$-friable integers up to $x$ when $y = (\log x)^C$ for a large constant $C$). In particular, we obtain an asymptotic formula for such Weyl sums in major arcs, nontrivial upper bounds for them in minor arcs, and moreover a mean value estimate for friable Weyl sums with exponent essentially the same as in the classical case. As an application, we study Waring's problem with friable numbers, with the number of summands essentially the same as in the classical case.
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Dates et versions

hal-01298060 , version 1 (24-01-2019)

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Sary Drappeau, Xuancheng Shao. Weyl sums, mean value estimates, and Waring's problem with friable numbers. Acta Arithmetica, 2016, 176, pp.249-299. ⟨10.4064/aa8448-7-2016⟩. ⟨hal-01298060⟩
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