The number of connected components of certain real algebraic curves
For an integer n≥2, let p(z)=∏k=1n(z−αk) and q(z)=∏k=1n(z−βk), where αk,βk are real. We find the number of connected components of the real algebraic curve {(x,y)∈ℝ2:|p(x+iy)|−|q(x+iy)|=0} for some αk and βk. Moreover, in these cases, we show that each connected component contains zeros of p(z)+q(z)...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010481 |
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