On the number of prime solutions to a system of quadratic equations
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...
| Main Author: | |
|---|---|
| Language: | English |
| Published: |
University of British Columbia
2013
|
| Online Access: | http://hdl.handle.net/2429/44283 |
| Summary: | 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. |
|---|