Results pertaining to the Sendov conjecture

[摘要] The Sendov conjecture may be stated: If all zeros of a complex polynomial p(z) lie in \z\ less than or equal to 1, then there is always a zero of p'(z), that is, a critical point of p(z), in \z - a\ less than or equal to 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. (C) 1997 Academic Press.

[发布日期] 1997-08-15