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University of Illinois at Urbana-Champaign

A new upper bound in the linear sieve and its applications

Abstract

dc:description

In 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 × 1

Rights

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

Chain of custody

source
Harvested from
University of Illinois - Urbana-Champaign
Base URL
www.ideals.illinois.edu/oai-pmh
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Lou, Shituo. A new upper bound in the linear sieve and its applications. Dissertation thesis, University of Illinois at Urbana-Champaign, 2011. http://hdl.handle.net/2142/19706