On the number of prime solutions to a system of quadratic equations

On the number of prime solutions to a system of quadratic equations

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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...

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Main Author: Fraser, Robert
Language:English
Published: University of British Columbia 2013
Online Access:http://hdl.handle.net/2429/44283
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-BVAU.2429-442832014-03-26T03:39:31Z On the number of prime solutions to a system of quadratic equations Fraser, Robert 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. 2013-04-18T14:01:34Z 2013-04-19T09:14:46Z 2013 2013-04-18 2013-05 Electronic Thesis or Dissertation http://hdl.handle.net/2429/44283 eng University of British Columbia
collection NDLTD
language English
sources NDLTD
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.
author Fraser, Robert
spellingShingle Fraser, Robert
On the number of prime solutions to a system of quadratic equations
author_facet Fraser, Robert
author_sort Fraser, Robert
title On the number of prime solutions to a system of quadratic equations
title_short On the number of prime solutions to a system of quadratic equations
title_full On the number of prime solutions to a system of quadratic equations
title_fullStr On the number of prime solutions to a system of quadratic equations
title_full_unstemmed On the number of prime solutions to a system of quadratic equations
title_sort on the number of prime solutions to a system of quadratic equations
publisher University of British Columbia
publishDate 2013
url http://hdl.handle.net/2429/44283
work_keys_str_mv AT fraserrobert onthenumberofprimesolutionstoasystemofquadraticequations
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