The Australian Journal of Mathematical Analysis and Applications

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Paper's Title:

On the Sendov Conjecture for a Root Close to the Unit Circle


Indraneel G. Kasmalkar

Department of Mathematics,
University of California,
Berkeley, CA 94720
United States of America



On Sendov's conjecture, T. Chijiwa quantifies the idea stated by V. Vājāitu and A. Zaharescu (and M. J. Miller independently), namely that if a polynomial with all roots inside the closed unit disk has a root sufficiently close to the unit circle then there is a critical point at a distance of at most one from that root. Chijiwa provides an estimate of exponential order for the required 'closeness' of the root to the unit circle so that such a critical point may exist. In this paper, we will improve this estimate to polynomial order by making major modifications and strengthening inequalities in Chijiwa's proof.

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