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Sommes friables d'exponentielles et applications
- Source :
- Canadian Journal of Mathematics, Canadian Journal of Mathematics, 2015, 67, pp.597-638. ⟨10.4153/CJM-2014-036-5⟩, Canadian Journal of Mathematics, University of Toronto Press, 2015, 67, pp.597-638. ⟨10.4153/CJM-2014-036-5⟩
- Publication Year :
- 2015
- Publisher :
- HAL CCSD, 2015.
-
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.<br />31 pages, in French
- 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
Subjects
Details
- Language :
- French
- ISSN :
- 0008414X
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics, Canadian Journal of Mathematics, 2015, 67, pp.597-638. ⟨10.4153/CJM-2014-036-5⟩, Canadian Journal of Mathematics, University of Toronto Press, 2015, 67, pp.597-638. ⟨10.4153/CJM-2014-036-5⟩
- Accession number :
- edsair.doi.dedup.....5522e5b7c4cc8206915bfef8dd74bdc2