On the representation of friable integers by linear forms
Résumé
Let $P^+(n)$ denote the largest prime of the integer $n$. Using the
\begin{align*}
\Psi_{F_1\cdots F_t}\left(\mathcal{K}\cap[-N,N]^d,N^{1/u}\right):=
\#\left\{\mathcal{K}\in {\mathbf{N}}\cap[-N,N]^d:\vphantom{P^+(F_1(\boldsymbol{n})\cdots F_t(\boldsymbol{n}))\leq N^{1/u}}\right.
\left.P^+(F_1(\boldsymbol{n})\cdots F_t(\boldsymbol{n}))\leq N^{1/u}\right\}
\end{align*}
where $(F_1,\ldots,F_t)$ is a system of affine-linear forms of $\mathbf{Z}[X_1,\ldots,X_d]$ no two
of which are affinely related and $\mathcal{K}$ is a convex body. This improves upon Balog, Blomer, Dartyge and Tenenbaum's work~\cite{BBDT12}
in the case of product of linear forms.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...