Abstract
The prime factorization of a random integer has a
GEM/Poisson-Dirichlet distribution as transparently proved by
Donnelly and Grimmett [8]. By similarity to the arc-sine
law for the mean distribution of the divisors of a random integer,
due to Deshouillers, Dress and Tenenbaum [6] (see also
Tenenbaum [24, II.6.2, p. 233]), – the ‘DDT
theorem’ – we obtain an arc-sine law in the
GEM/Poisson-Dirichlet context. In this context we also
investigate the distribution of the number of components larger than
ε which correspond to the number of prime factors larger than
nε.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
6 articles.
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