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A three dimensional set of limit points related to the abc Conjecture Simpson, Reginald M.
Abstract
We study the limit points Q' of a three-dimensional set Q which encodes the reciprocal quality of abc triples as the components of a vector of the form (log Rad a, log Rad b, log Rad c) / log c. We establish that if the abc Conjecture holds, Q' is contained in a heptahedron. Unconditionally, we establish the existence of a subset of Q' with non-zero measure. We determine the implications of previous research on related problems involving limit points of abc triples in one-dimensional sets on Q' and discuss possible avenues for future study.
Item Metadata
| Title |
A three dimensional set of limit points related to the abc Conjecture
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2017
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| Description |
We study the limit points Q' of a three-dimensional set Q which encodes the reciprocal quality
of abc triples as the components of a vector of the form (log Rad a, log Rad b, log Rad c) / log c. We establish that if the abc Conjecture holds, Q' is contained in a heptahedron. Unconditionally, we establish the existence of a subset of Q' with non-zero measure. We determine the implications of previous research on related problems involving limit points of abc triples in one-dimensional sets on Q' and discuss possible avenues for future study.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2017-12-23
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0362415
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2018-02
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International