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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 haveD(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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