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arXiv · 2001.04435

Entiers ultrafriables en progressions arithm\'etiques

Cécile Dartyge·David Feutrie·Gérald Tenenbaum
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Abstract

A natural integer is called $y$-ultrafriable if none of the prime powers occurring in its canonical decomposition exceed $y$. We investigate the distribution of $y$-ultrafriable integers not exceeding $x$ among arithmetic progressions to the modulus $q$. Given a sufficiently small, positive constant $\varepsilon$, we obtain uniform estimates valid for $q\leqslant y^{c/\log_2y}$ whenever $\log y\leqslant (\log x)^\varepsilon$, and for $q\leqslant \sqrt{y}$ if $(\log x)^{2+\varepsilon}\leqslant y\leqslant x$.

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BibTeXRIS

Cécile Dartyge, David Feutrie, Gérald Tenenbaum. 2020-01-13. Entiers ultrafriables en progressions arithm\'etiques. https://arxiv.org/abs/2001.04435

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