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Results Pertaining to the Sendov Conjecture

✍ Scribed by Angelina Byrne

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 157 KB
Volume: 212
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5500

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✦ Synopsis

The Sendov conjecture may be stated: If all zeros of a complex polynomial p z < < X Ž . Ž . lie in z F 1, then there is always a zero of p z , that is, a critical point of p z , in < < Ž . z y a F 1, where a is any zero of p z . We prove several cases for which the Sendov conjecture is true as well as some stronger results. The case where a is the root with pth largest modulus is also investigated.

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