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UBC Theses and Dissertations

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.

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