STATISTICS OF SIEVES AND SQUARE-FREE NUMBERS

Let L = (s1,s2,...) be a collection of relatively prime numbers. The asymptotic properties of the process of sieving by L may be realized in terms of a stationary random process. In the case when L is the set of squares of the primes, one may make use of this representation to verify a conjecture of R. Hall: in a 'typical' interval of length k, the number S(k) of square-free numbers has a probability mass function having order k-1/4 in the limit of k --> infinity.