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Divisors of Bernoulli Sums
Authors:Michel Weber
Affiliation:(1) U.F.R. de Mathématique (IRMA), Université Louis-Pasteur et C.N.R.S., 7 rue René Descartes, F-67084 Strasbourg Cedex, France
Abstract:Let 
$$B_{n} = b_{1} + cdots + b_n, n geq 1$$
where 
$$b_1, b_2,cdots$$
are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic order of the sums 
$$sumnolimits_{n=1}^{N}{d_{theta, {mathcal{D}}}(B_n)}$$
, where 
$$d_{theta,{mathcal{D}}}(B_n)= # {d in mathcal{D},d leq n^{theta}:dmid B_n}$$
and 
$${mathcal{D}}$$
is a sequence of positive integers. Received: May 23, 2007. Revised: June 8, 2007.
Keywords:Primary 11M06  Secondary 11M99, 11A25, 60G50
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