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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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