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University of Illinois at Urbana-Champaign
A new upper bound in the linear sieve and its applications
Abstract
dc:descriptionIn Chapter I we shall prove a new upper bound in the linear sieve. Our purpose in Chapter II is to explain our method in greater detail than was done in Chapter I. Let x be a large number. We consider π\sb2(x)--the number of prime twins not exceeding x. Using the new upper bound in the linear sieve from Chapter I, we shall prove that$\rmπ\sb2({x}) 0 and x $\geq$ x\sb0(ε), where$$\rm H = 2{\prod\limits\sb{p>2}}\left(1-{1\over(p-1)\sp2}\right).$$In the Appendix, various computations cited in the text are given in detail.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Lou, Shituo
- Contributors dc:contributor
-
- Diamond, Harold G.
Subjects
dc:subject × 1Rights
dc:rights- Statement dc:rights
-
- Copyright 1990 Lou, Shituo
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
-
AAI9021722
(UMI)AAI9021722 - OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/19706