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MAHLER MEASURE OF ‘ALMOST’ RECIPROCAL POLYNOMIALS

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  03 May 2018

J. C. SAUNDERS
J. C. SAUNDERS*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada email [email protected]
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Abstract

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We give a lower bound of the Mahler measure on a set of polynomials that are ‘almost’ reciprocal. Here ‘almost’ reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern may break down for the innermost coefficients.

Keywords

Lehmer’s conjectureMahler measurenumber theorypolynomials

MSC classification

Primary: 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
Secondary: 11R09: Polynomials (irreducibility, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 70 - 76
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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