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Sommes friables d'exponentielles et applications

  Published:2015-02-17
 Printed: Jun 2015
  • Sary Drappeau,
    Université Paris Diderot - Paris 7, Institut de Mathématiques de Jussieu--Paris Rive Gauche, UMR 7586, Bâtiment Chevaleret, Bureau 7C08, 75205 Paris Cedex 13
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Abstract

An integer is said to be $y$-friable if its greatest prime factor is less than $y$. In this paper, we obtain estimates for exponential sums over $y$-friable numbers up to $x$ which are non-trivial when $y \geq \exp\{c \sqrt{\log x} \log \log x\}$. As a consequence, we obtain an asymptotic formula for the number of $y$-friable solutions to the equation $a+b=c$ which is valid unconditionnally under the same assumption. We use a contour integration argument based on the saddle point method, as developped in the context of friable numbers by Hildebrand and Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers.
Keywords: théorie analytique des nombres, entiers friables, méthode du col théorie analytique des nombres, entiers friables, méthode du col
MSC Classifications: 12N25, 11L07 show english descriptions unknown classification 12N25
Estimates on exponential sums
12N25 - unknown classification 12N25
11L07 - Estimates on exponential sums
 

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