On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial
Canadian mathematical bulletin, Tome 30 (1987) no. 4, pp. 476-480
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Let P be a polynomial of degree n having all its zeros in the closed unit disk. Given that a is a zero (of P) of multiplicity k we seek to determine the radius ρ(n; k; a) of the smallest disk centred at a containing at least k zeros of the derivative P'. In the case k = 1 the answer has been conjectured to be 1 and is known to be true for n ≦ 5. We prove that ρ(n; k; a) ≦ 2k/(k + 1) for arbitrary k ∊ N and n ≦ k + 4.
Rahman, Q. I.; Tariq, Q. M. On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial. Canadian mathematical bulletin, Tome 30 (1987) no. 4, pp. 476-480. doi: 10.4153/CMB-1987-070-9
@article{10_4153_CMB_1987_070_9,
author = {Rahman, Q. I. and Tariq, Q. M.},
title = {On a {Problem} {Related} to {The} {Conjecture} of {Sendov} {About} {The} {Critical} {Points} of a {Polynomial}},
journal = {Canadian mathematical bulletin},
pages = {476--480},
year = {1987},
volume = {30},
number = {4},
doi = {10.4153/CMB-1987-070-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-070-9/}
}
TY - JOUR AU - Rahman, Q. I. AU - Tariq, Q. M. TI - On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial JO - Canadian mathematical bulletin PY - 1987 SP - 476 EP - 480 VL - 30 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-070-9/ DO - 10.4153/CMB-1987-070-9 ID - 10_4153_CMB_1987_070_9 ER -
%0 Journal Article %A Rahman, Q. I. %A Tariq, Q. M. %T On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial %J Canadian mathematical bulletin %D 1987 %P 476-480 %V 30 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-070-9/ %R 10.4153/CMB-1987-070-9 %F 10_4153_CMB_1987_070_9
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