The number of connected components of certain real algebraic curves

Seon-Hong Kim

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-9

Abstract:

For an integer n ≥ 2 , let p ( z ) = ∏ k = 1 n ( z − α k ) and q ( z ) = ∏ k = 1 n ( z − β k ) , where α k , β k are real. We find the number of connected components of the real algebraic curve { ( x , y ) ∈ ℝ 2 : | p ( x + i y ) | − | q ( x + i y ) | = 0 } for some α k and β k . 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 ) .

Date: 2001
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/25/292497.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/25/292497.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:292497

DOI: 10.1155/S0161171201010481

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().