On the representation of friable integers by linear forms

DOI10.4064/AA8153-9-2017zbMATH Open1429.11180arXiv1609.08872OpenAlexW2962908124MaRDI QIDQ4595447

Armand Lachand

Publication date: 30 November 2017

Published in: Acta Arithmetica (Search for Journal in Brave)

Abstract: Let $P^{+}(n)$ denote the largest prime of the integer $n$. Using the �egin{align*}Psi_{F_1cdots F_t}left(mathcal{K}cap[-N,N]^d,N^{1/u} ight):=\#left{mathcal{K}in {mathbf{N}}cap[-N,N]^d:vphantom{P^+(F_1(�oldsymbol{n})cdots F_t(�oldsymbol{n}))leq N^{1/u}} ight.left.P^+(F_1(�oldsymbol{n})cdots F_t(�oldsymbol{n}))leq N^{1/u} ight}end{align*} where $(F_1,ldots,F_t)$ is a system of affine-linear forms of $mathbfZ[X_1,ldots,X_d]$ no two of which are affinely related and $mathcalK$ is a convex body. This improves upon Balog, Blomer, Dartyge and Tenenbaum's work~cite{BBDT12} in the case of product of linear forms.

Full work available at URL: https://arxiv.org/abs/1609.08872

zbMATH Keywords

linear formsGowers normsfriable integers

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution of integers with specified multiplicative constraints (11N25)

Related Items (1)

Linear correlations of multiplicative functions

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