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Divisors of Bernoulli Sums

Authors:	Michel Weber

Institution:	(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 $\sum\nolimits_{n=1}^{N}{d_{\theta, {\mathcal{D}}}(B_n)}$ , where $d_{\theta,{\mathcal{D}}}(B_n)= \# \{d \in \mathcal{D},d \leq n^{\theta}:d\mid B_n\}$ 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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