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Bulletin of the London Mathematical Society Advance Access originally published online on August 13, 2008
Bulletin of the London Mathematical Society 2008 40(6):956-964; doi:10.1112/blms/bdn076
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© 2008 London Mathematical Society

An inequality for the modulus of a polynomial evaluated at the roots of unity

T. Sheil-Small

P.O. Box 60681
CY8106 Paphos
Cyprus

Received 31 October 2007. Revision received 29 May 2008.

It is shown that if P(z) is an analytic polynomial of degree n and if N is a natural number with N>n, then Formula , where {omega} runs through the Nth roots of unity.

2000 Mathematics Subject Classification 30C10, 42A15.


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