论文标题
Entiers Ultrafriables enarithmétiques
Entiers ultrafriables en progressions arithmétiques
论文作者
论文摘要
自然整数称为$ y $ ultrafraif，如果其规范分解中的主要力量都超过$ y $。我们调查了算术进展中不超过$ x $的$ y $ ultrafraifer整数的分布。给定一个足够小的，正常数的$ \ varepsilon $，我们获得均匀的估计值，对于$ q \ leqslant y^{c/\ log_2y} $ x）^{2+ \ varepsilon} \ leqslant y \ leqslant x $。
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 $(\log x)^{2+\varepsilon}\leqslant y\leqslant x$.
