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On the number of prime solutions to a system of quadratic equations Fraser, Robert
Abstract
Consider the system of quadratic diophantine equations bX² − aY² = 0 bX • Y − eY² = 0 constrained to the prime numbers contained in the box [0,N]²ⁿ. The Hardy- Littlewood circle method is applied to show that, under some local conditions on a, b, and e, the number of prime solutions contained in the box is asymptotic to a constant times N²ⁿ⁻⁴/ (logN)²ⁿ , where the constant depends on a, b, and e.
Item Metadata
| Title |
On the number of prime solutions to a system of quadratic equations
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2013
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| Description |
Consider the system of quadratic diophantine equations
bX² − aY² = 0
bX • Y − eY² = 0
constrained to the prime numbers contained in the box [0,N]²ⁿ. The Hardy-
Littlewood circle method is applied to show that, under some local conditions on a, b, and e, the number of prime solutions contained in the box is asymptotic to a constant times N²ⁿ⁻⁴/ (logN)²ⁿ , where the constant depends on a, b, and e.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2013-04-19
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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 |
10.14288/1.0071953
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2013-05
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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