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Description
Title: | Localization of Divisors of Integers and of Some Arithmetic Functions |
Author(s): | Hu, Yong |
Doctoral Committee Chair(s): | Kevin Ford |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | We investigate several problems related to the multiplicative structure of integers. First, we determine the order of magnitude of the function H2(x, y, z), the number of positive integers n ≤ x having exactly two divisors in ( y, z], in the range of y10 ≤ z ≤ x1/3, and that of the function H3(x, y, z), the number of positive integers n ≤ x having exactly three divisors in ( y, z], in the range of y10 ≤ z ≤ x1/4. Next, we introduce a new function H1,1(x, y, z 1, z2), the number of positive integers n ≤ x having one divisor in (y, z 1] and one divisor in (z1, z 2] and study its order of magnitude. Finally, we investigate problems about localization of divisors of the Euler function &phis;(n) and the Carmichael function lambda(n). We say that a positive integer m is u-dense if whenever 1 ≤ y ≤ m, there is a divisor of m in the interval (y, uy]. We show that for > x integers n ≤ x, both &phis;(n) and lambda(n) are 2-dense. |
Issue Date: | 2007 |
Type: | Text |
Language: | English |
Description: | 71 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. |
URI: | http://hdl.handle.net/2142/86883 |
Other Identifier(s): | (MiAaPQ)AAI3290250 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 2007 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois