Skip Navigation

Journal of the London Mathematical Society 1991 s2-43(1):1-11; doi:10.1112/jlms/s2-43.1.1
© 1991 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Grimmett, G.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© Oxford University Press

Statistics of Sieves and Square-Free Numbers

Geoffrey Grimmett

School of Mathematics, University Walk Bristol BS8 1TW

Let S = (s1, s2,...) be a collection of relatively prime numbers. The asymptotic properties of the process of sieving by S may be realized in terms of a stationary random process. In the case when S 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 Sk of square-free numbers has a probability mass function having order k –1/4 in the limit as k -> {infty}.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.