Geodesic
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

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1987-070-9
Mots-clés : 30C15 (Primary) 
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
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