The Number of Connected Components of Certain Real Algebraic Curves
نویسنده
چکیده
For an integer n≥ 2, let p(z)=nk=1(z−αk) and q(z)= ∏n k=1(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), and we investigate the locus of zeros of p(z)+q(z). 2000 Mathematics Subject Classification. Primary 26C10; Secondary 30C15.
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