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- W1997891615 abstract "Let Ψ ( x , y ) denote the number of positive integers ≦ x and free of prime factors > y . De Bruijn showed that the relation Ψ(x, x 1 u ) ∼ xϱ(u) holds, as x → ∞, uniformly in the range 1 ≦ u ≦ ( log x) 3 8 − ϵ . We extend this range to 1 ≦ u ≦ log x ( log log x) 5 3 + ϵ , and give a similar, but weaker estimate for the range 1 ≦ u ≦ log x (1 + ϵ) log log x . We also prove a short interval result." @default.
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- W1997891615 date "1986-03-01" @default.
- W1997891615 modified "2023-10-12" @default.
- W1997891615 title "On the number of positive integers ≦ x and free of prime factors > y" @default.
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- W1997891615 doi "https://doi.org/10.1016/0022-314x(86)90013-2" @default.
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