The Journal of the Indian Mathematical Society

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Some Results Concerning Sendov Conjecture


Affiliations
1 Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
     

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Let P(z) be a complex polynomial of degree n having all its zeros in |z| ≤ 1. Then the Sendov’s Conjecture states that there is always a critical point of P(z) in |z − a| ≤ 1, where a is any zero of P(z). In this paper, we verify the Sendov’s Conjecture for some special cases. The case where a is the root of pth smallest modulus is also investigated.


Keywords

Polynomial, Disk, Zeros, Critical Point, Transformation.
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  • Some Results Concerning Sendov Conjecture

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Authors

Mohammad Ibrahim Mir
Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
Ishfaq Nazir
Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
Irfan Ahmad Wani
Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India

Abstract


Let P(z) be a complex polynomial of degree n having all its zeros in |z| ≤ 1. Then the Sendov’s Conjecture states that there is always a critical point of P(z) in |z − a| ≤ 1, where a is any zero of P(z). In this paper, we verify the Sendov’s Conjecture for some special cases. The case where a is the root of pth smallest modulus is also investigated.


Keywords


Polynomial, Disk, Zeros, Critical Point, Transformation.

References