Sommes friables d'exponentielles et applications

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 $y\ge \exp \{c\sqrt{\log x}\log \log x\}$. 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

References in corpus (2)

• Counting Smooth Solutions to the Equation A+B=C
• Sur les solutions friables de l'équation a+b=c

Cited by in corpus (1)

• Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers