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Polynomials with Restricted Coefficients and Prescribed Noncyclotomic Factors

Published online by Cambridge University Press:  01 February 2010

Michael J. Mossinghoff
Michael J. Mossinghoff
Affiliation:
Department of Mathematics, Davidson College, Davidson, NC 28035, USA [email protected], http://www.davidson.edu/math/mossinghoff

Abstract

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The algorithms described in this paper were developed to investigate three problems regarding polynomials with restricted coefficients: (i) determining whether there exist polynomials with {0, 1} coefficients and repeated noncyclotomic factors, (ii) searching for polynomials with {−1, 1} coefficients and small Mahler measure, and (iii) finding polynomials with {−1, 0, 1} coefficients with a root of high multiplicity off the unit circle. The results in the first problem presented here answer a question of Odlyzko and Poonen.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 6 , 2003 , pp. 314 - 325
Copyright
Copyright © London Mathematical Society 2003

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