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Title:A new upper bound in the linear sieve and its applications
Author(s):Lou, Shituo
Doctoral Committee Chair(s):Diamond, Harold G.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract: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 $\pi\sb2$(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$$\rm\pi\sb2({x}) 0$ and x $\geq$ x$\sb0(\epsilon),$ where$$\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.
Issue Date:1990
Type:Text
Language:English
URI:http://hdl.handle.net/2142/19706
Rights Information:Copyright 1990 Lou, Shituo
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9021722
OCLC Identifier:(UMI)AAI9021722


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