The number of connected components of certain real algebraic curves
نویسندگان
چکیده
منابع مشابه
The Number of Connected Components of Certain Real Algebraic Curves
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 Classificati...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2001
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171201010481