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Zeros of Harmonic Polynomials
by
Bruce Crofoot
University College of the Cariboo (British Columbia, Canada)
Coauthors: Donald Sarason
It has been conjectured that if p(z) is a polynomial in the complex variable z, of degree n > 1, then the equation p(z)=[`z] (where [`z] denotes the conjugate of z) has at most 3n-2 distinct solutions. I will outline a proof of this conjecture for the case n=3 and discuss progress and obstacles in extending the ideas of this proof to the general case.
Date received: April 20, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacb-22.