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  • 1
    Electronic Resource
    Electronic Resource
    On the integersn for which Ω(n)=k (II) (1993)
    Springer
    Monatshefte für Mathematik 116 (1993), S. 175-196 
    Details
    ISSN: 1436-5081
    Keywords: 10K99 ; 10H15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let Ω(n) be the number of prime divisors ofn, counted with multiplicity. We denote byS(x, k) the set of then≤x for which Ω(n)=k, and byV p(n) the exponent of the primep in the factorization ofn. In a previous paper we proved a result which implies that, ify=x/2 k tends to infinity withk〉2λloglogx where λ〉1, then the distribution of the numbers $$(V_2 (n) - k + 2\log \log y)/\sqrt {2 \log \log y} $$ on the setS(x, k) converges to the normal distribution of Gauss. Here, besides a slight improvement of that result, we give, for the moment of orderq of the above mentioned distribution, a formula which holds uniformly for 2λloglogx≤k≤log (x/3)/log2 where 1〈λ〈3/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01301527
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