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arXiv · 1506.03268

Entiers friables dans des progressions arithm\'etiques de grand module

Régis de la Bretèche·Daniel Fiorilli
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Abstract

We study the average error term in the usual approximation to the number of $y$-friable integers congruent to $a$ modulo $q$, where $a\neq 0$ is a fixed integer. We show that in the range $\exp\{(\log\log x)^{5/3+\varepsilon}\} \leq y \leq x$ and on average over $q\leq x/M$ with $M\rightarrow \infty$ of moderate size, this average error term is asymptotic to $-|a|\Psi(x/|a|,y)/2x$. Previous results of this sort were obtained by the second author for reasonably dense sequences, however the sequence of $y$-friable integers studied in the current paper is thin, and required the use of different techniques, which are specific to friable integers.

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Régis de la Bretèche, Daniel Fiorilli. 2015-06-10. Entiers friables dans des progressions arithm\'etiques de grand module. https://arxiv.org/abs/1506.03268

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