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A new upper bound in the linear sieve and its applications

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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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