


Paper Title:
On the Sendov Conjecture for a Root Close to the Unit Circle
Author(s):
Indraneel G. Kasmalkar
Department of Mathematics,
University of California,
Berkeley, CA 94720
United States of America
Email: indraneelk@berkeley.edu
Abstract:
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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