Entiers ultrafriables en progressions arithmétiques
Résumé
A natural integer is calledy-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 ε, we obtain uniform estimates valid for q≤y^{c/log_2y} whenever logy≥(logx)^ε, and for q≤√y if (logx)^{2+ε} ≤ y ≤ x
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