Generalized Smirnov statistics and the distribution of prime factors

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Generalized Smirnov Statistics and the Distribution of Prime Factors

(1.2) log2 pj ≤ αj + β (1 ≤ j ≤ ω(n)), where α ≥ 0 and log2 y denotes log log y. The distribution of integers satisfying (1.1) is important in the study of the distribution of divisors of integers (see [3]; Ch. 2 of [4]). We present here estimates for Nk(x;α, β) = #{n ≤ x : ω(n) = k, (1.1)}, Mk(x;α, β) = #{n ≤ x : ω(n) = k, (1.2)}. It is a relatively simple matter, at least heuristically, to re...

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ژورنال

عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici

سال: 2007

ISSN: 0208-6573

DOI: 10.7169/facm/1229618745