Mathematical Proceedings of the Cambridge Philosophical Society

作者：Hough Bob^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2011, 150: 193-214.

DOI：10.1017/S0305004110000514

Given a +/- 1 random completely multiplicative function f, we prove by estimating moments that the limiting distribution of the normalized sum
1/root Var Sigma(r)(n<x) f(n)
converges to the standard Gaussian distribution as x -> infinity when r restricts summation to n having o(log log log x) prime factors. We also give an upper bound for the large deviations of
Sigma(k)(n<x) f(n),
with the sum restricted to numbers having a fixed number k of prime factors.

• 出版日期2011-3