Geodesic
Weyl sums, mean value estimates, and Waring's problem with friable numbers
Sary Drappeau 1   ; Xuancheng Shao 2
1 Aix-Marseille Université, CNRS Centrale Marseille I2M UMR 7373 13453 Marseille Cedex, France
2 Mathematical Institute Radcliffe Observatory Quarter Woodstock Road Oxford OX2 6GG, United Kingdom
Acta Arithmetica, Tome 176 (2016) no. 3, pp. 249-299 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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, non-trivial 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.
DOI : 10.4064/aa8448-7-2016
Keywords: paper study weyl sums friable integers precisely y friable integers nbsp nbsp log large constant nbsp particular obtain asymptotic formula weyl sums major arcs non trivial upper bounds minor arcs moreover mean value estimate friable weyl sums exponent essentially the classical application study waring problem friable numbers number summands essentially the classical

Sary Drappeau  1   ; Xuancheng Shao  2

1 Aix-Marseille Université, CNRS Centrale Marseille I2M UMR 7373 13453 Marseille Cedex, France
2 Mathematical Institute Radcliffe Observatory Quarter Woodstock Road Oxford OX2 6GG, United Kingdom 
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     title = {Weyl sums, mean value estimates, and {Waring's} problem with friable numbers},
     journal = {Acta Arithmetica},
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Sary Drappeau; Xuancheng Shao. Weyl sums, mean value estimates, and Waring's problem with friable numbers. Acta Arithmetica, Tome 176 (2016) no. 3, pp. 249-299. doi: 10.4064/aa8448-7-2016

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