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Title:On the Distribution Function of N/phi(n)
Author(s):Rhoads, Dennis Lynn
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Let (phi)(n) denote Euler's function and let D(x) denote the distribution function of
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
i.e.,
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
A method is developed for numerically approximating D(x) based on a series expansion of D(x).
An estimate of the modulus of continuity of D(x) is also established. In this regard, the following result is established.
Theorem. There exists an absolute constant c such that for 0 0 we have
D(x+(epsilon)x) - D(x) < c/log(1/(epsilon)).
Issue Date:1981
Type:Text
Description:91 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.
URI:http://hdl.handle.net/2142/71200
Other Identifier(s):(UMI)AAI8203565
Date Available in IDEALS:2014-12-16
Date Deposited:1981


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