A new upper bound in the linear sieve and its applications
Lou, Shituo
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https://hdl.handle.net/2142/19706
Description
Title
A new upper bound in the linear sieve and its applications
Author(s)
Lou, Shituo
Issue Date
1990
Doctoral Committee Chair(s)
Diamond, Harold G.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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