On the Sendov Conjecture for Polynomials with at Most Six Distinct Roots

✍ Scribed by Iulius Borcea

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 229 KB
• Volume: 200
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0198

✦ Synopsis

In this paper we prove that Sendov's conjecture is true for polynomials of degree Ž . n s 6 we even determine the so-called extremal polynomials in this case , as well as for polynomials with at most six different zeros. We then generalize this last Ž . Ž . result to polynomials of degree n with at most n distinct roots, where n is an increasing and unbounded function of n.