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UBC Theses and Dissertations
Thue equations Ghadermarzi, Amir
Abstract
In this dissertation, we are mainly interested in effective methods to solve parametrized Thue equations. After briefly talking about the different effective methods, two parametrized families of cubic Thue equations are completely solved by using Pad é approximation and linear forms in logarithms. The Thue inequality ∣x³ + pxy² + qy³ ∣≤ k, is studied by using Bombieri's method. We find all solutions under some conditions on k, p and q. As an application of Thue equations, we find the integral points on the Mordell curves Y² = X³ + k for all nonzero integers k with ∣k∣ ≤ 10⁷ . Our approach uses a classical connection between these equations and cubic Thue equations.
Item Metadata
| Title |
Thue equations
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2014
|
| Description |
In this dissertation, we are mainly interested in effective methods to solve
parametrized Thue equations. After briefly talking about the different effective methods, two parametrized families of cubic Thue equations are completely
solved by using Pad é approximation and linear forms in logarithms.
The Thue inequality
∣x³ + pxy² + qy³ ∣≤ k,
is studied by using Bombieri's method. We find all solutions under some conditions on k, p and q. As an application of Thue equations, we find the
integral points on the Mordell curves Y² = X³ + k for all nonzero integers
k with ∣k∣ ≤ 10⁷ . Our approach uses a classical connection between these
equations and cubic Thue equations.
|
| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2014-01-10
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0166844
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2014-05
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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