From the same journal

From the same journal

THE ASYMPTOTICS OF RANDOM SIEVES

Research output: Contribution to journalArticle

Author(s)

  • G R Grimmett
  • Richard Hall

Department/unit(s)

Publication details

JournalMathematika
DatePublished - Dec 1991
Issue number76
Volume38
Number of pages18
Pages (from-to)285-302
Original languageEnglish

Abstract

Let T = (s1, s2,...) be a collection of relatively prime integers, and suppose that pi(n) = /T the-intersection-of {1,2,...,n}\ is a regularly varying function with index alpha -atisfying 0 < alpha < 1. We investigate the "stationary random sieve" generated by T, proving that the number of integers less than k which escape the action of the sieve has a probability mass function with approximate order k-alpha/2 in the limit as k --> infinity. This result may be used to deduce certain asymptotic properties of the set of integers which are divisible by no s is-an-element-of T, in that it gives new information about the usual deterministic (that is, non-random) sieve. This work extends previous results valid when s(i) = p(i)2, the square of the ith prime.

    Research areas

  • NUMBER THEORY, MULTIPLICATIVE NUMBER THEORY, DISTRIBUTION OF INTEGERS WITH SPECIFIED MULTIPLICATIVE CONSTRAINTS, SQUAREFREE NUMBERS

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