1992
DOI: 10.1112/blms/24.5.449
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On the Sendov-Ilyeff Conjecture

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Cited by 4 publications
(6 citation statements)
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References 13 publications
(26 reference statements)
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“…[7]). A similar theorem is proved in [6] as well, only the upper bound obtained there is somewhat weaker. 1 + mm ln(n -(n -l)a) o<a<i ln(l+a-a2) then I{p) < 1, unless n < 4 and p(z) = z" -e' ® for some real 6 ([..] denotes here the integral pari and the function between brackets is defined as n -1 for a = 1).…”
Section: Preliminary Results and Notationsupporting
confidence: 66%
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“…[7]). A similar theorem is proved in [6] as well, only the upper bound obtained there is somewhat weaker. 1 + mm ln(n -(n -l)a) o<a<i ln(l+a-a2) then I{p) < 1, unless n < 4 and p(z) = z" -e' ® for some real 6 ([..] denotes here the integral pari and the function between brackets is defined as n -1 for a = 1).…”
Section: Preliminary Results and Notationsupporting
confidence: 66%
“…Various other special cases have been dealt with (see [3], [9], and [18] for references), the latest to date being that of polynomials with at most six different zeros, and more generally polynomials in P"(i/(n)), where v{n) is an increasing and unbounded function of n (Theorem 2.4 below) (cf. [2]; see also [6]). …”
Section: Introductionmentioning
confidence: 91%
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“…1 We set R s and A s 0.562. Since p is extremal and G 1, we 9 9 j 2 assert that it must have the form < To verify this we set r s a y z and note that since z is repeated 0 0 Ž . r s r s r s , Re z G 0 and G 1, we must have…”
Section: žmentioning
confidence: 99%