Details

Philipp Habegger ^[a]

Separating roots of polynomials and the transfinite diameter

Pages: 111-136
Received: 25 May 2021
Accepted in revised form: 27 October 2021
Mathematics Subject Classification: 12D10, 11C08, 30C85.
Keywords: Root separation of complex polynomials, discriminant, transfinite diameter.
Authors address:
[a]: Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051 Basel, Switzerland.

The author has received funding from the Swiss National Science Foundation project n\(^\circ\) 200020_184623.

Abstract: Mahler proved a lower bound for the distance between distinct roots of a squarefree complex polynomial. We extend his result to packets of tuples of complex roots and slightly improve a numerical constant. One application of the former aspect is an upper bound for the transfinite diameter of certain star-shaped compact subsets of the complex plane.

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