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Summation of a random multiplicative function on numbers having few prime factors

Published online by Cambridge University Press:  13 December 2010

BOB HOUGH
BOB HOUGH*
Affiliation:
Department of Mathematics, Stanford University, Building 380, Stanford, CA 94305, U.S.A. e-mail: [email protected]
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Abstract

Given a ±1 random completely multiplicative function f, we prove by estimating moments that the limiting distribution of the normalized sumconverges to the standard Gaussian distribution as x → ∞ when r restricts summation to n having o(log log log x) prime factors. We also give an upper bound for the large deviations ofwith the sum restricted to numbers having a fixed number k of prime factors.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 2 , March 2011 , pp. 193 - 214
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

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