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Prime symmetric divisor functions Woodford, Roger
Abstract
In this thesis, we study a new class of divisor-related functions: the prime symmetric functions. The elementary prime symmetric functions are denned on the nonnegative integers. They take the values of the elementary symmetric functions applied to the multi-set of prime factors with repetition of an integer n. These functions are first defined i n [20]. In this thesis, we refine some of the definitions presented there, and revisit some of the key results regarding such functions. The prime symmetric functions are polynomials over Q in the elementary prime symmetric functions, with values in Z. We look at basic properties of prime symmetric functions. We study the effect of iteration of these functions, and look at the question: when does iterating produce cycles? We consider the inverse question of when and in how many ways a number n can be expressed as f(m) for certain predetermined prime symmetric functions. As well, we look at asymptotic approximations for certain classes of prime symmetric functions.
Item Metadata
Title |
Prime symmetric divisor functions
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2005
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Description |
In this thesis, we study a new class of divisor-related functions: the prime symmetric
functions. The elementary prime symmetric functions are denned on the nonnegative
integers. They take the values of the elementary symmetric functions applied
to the multi-set of prime factors with repetition of an integer n. These functions are
first defined i n [20]. In this thesis, we refine some of the definitions presented there,
and revisit some of the key results regarding such functions. The prime symmetric
functions are polynomials over Q in the elementary prime symmetric functions, with
values in Z. We look at basic properties of prime symmetric functions. We study the
effect of iteration of these functions, and look at the question: when does iterating
produce cycles? We consider the inverse question of when and in how many ways a number n can be expressed as f(m) for certain predetermined prime symmetric
functions. As well, we look at asymptotic approximations for certain classes of
prime symmetric functions.
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Genre | |
Type | |
Language |
eng
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Date Available |
2009-12-16
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080069
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2005-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.