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A Note on Lawton's Theorem

Published online by Cambridge University Press:  20 November 2018

Edward Dobrowolski
Edward Dobrowolski*
Affiliation:
Mathematics Department, University of Northern British Columbia, Prince George, BC. e-mail: edward.dobrowolski@unbc.ca
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Abstract

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We prove Lawton's conjecture about the upper bound on themeasure of the set on the unit circle on which a complex polynomial with a bounded number of coefficients takes small values. Namely, we prove that Lawton's bound holds for polynomials that are not necessarily monic. We also provide an analogous bound for polynomials in several variables. Finally, we investigate the dependence of the bound on the multiplicity of zeros for polynomials in one variable.

Keywords

11R0911R06polynomialMahler measure
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 484 - 489
Copyright
Copyright © Canadian Mathematical Society 2017

References

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