University of Illinois Urbana-Champaign

On the Distribution Function of N/phi(n)

Rhoads, Dennis Lynn

This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.

Permalink

https://hdl.handle.net/2142/71200

Description

Title
On the Distribution Function of N/phi(n)
Author(s)
Rhoads, Dennis Lynn
Issue Date
1981
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
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.,
  • 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)).
Graduation Semester
1981
Type of Resource
text
Permalink
http://hdl.handle.net/2142/71200

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics