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arXiv · 1302.4318

Sommes friables d'exponentielles et applications

Sary Drappeau
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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 & Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers.

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Sary Drappeau. 2013-02-18. Sommes friables d'exponentielles et applications. https://doi.org/10.4153/cjm-2014-036-5

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