Weyl sums, mean value estimates, and Waring's problem with friable numbers
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
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.
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
Affiliations des auteurs :
Sary Drappeau 1 ; Xuancheng Shao 2
@article{10_4064_aa8448_7_2016,
author = {Sary Drappeau and Xuancheng Shao},
title = {Weyl sums, mean value estimates, and {Waring's} problem with friable numbers},
journal = {Acta Arithmetica},
pages = {249--299},
year = {2016},
volume = {176},
number = {3},
doi = {10.4064/aa8448-7-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8448-7-2016/}
}
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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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