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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Limit theorems for divisor distributions


Author: Michael D. Vose
Journal: Proc. Amer. Math. Soc. 95 (1985), 505-511
MSC: Primary 11N60; Secondary 11K65
MathSciNet review: 810153
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Abstract: For a positive integer $ N$, let $ {X_N}$ be a random variable uniformly distributed over the set $ \{ \log d:d\vert N\} $. Let $ {F_N}$ be the normalized (to have expectation zero and variance one) distribution function for $ {X_N}$. Necessary and sufficient conditions for the convergence of a sequence $ {F_{{N_j}}}$ of distributions are given. The possible limit distributions are investigated, and the case where the limit distribution is normal is considered in detail.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0810153-0
PII: S 0002-9939(1985)0810153-0
Article copyright: © Copyright 1985 American Mathematical Society