1. Sommes friables d'exponentielles et applications
- Author
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Sary Drappeau, Équipe de th. des nombres, Institut de Mathématiques de Jussieu (IMJ), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Mathematics - Number Theory ,General Mathematics ,010102 general mathematics ,Context (language use) ,0102 computer and information sciences ,01 natural sciences ,Methods of contour integration ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Exponential function ,Combinatorics ,Character (mathematics) ,Integer ,010201 computation theory & mathematics ,11L07, 11N25 (primary), 11M06, 11L40, 11D45 ,Saddle point ,Prime factor ,FOS: Mathematics ,Asymptotic formula ,Number Theory (math.NT) ,0101 mathematics ,Mathematics - 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 & Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers., 31 pages, in French
- Published
- 2015