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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Resultants and discriminants of Chebyshev and related polynomials


Authors: Karl Dilcher and Kenneth B. Stolarsky
Journal: Trans. Amer. Math. Soc. 357 (2005), 965-981
MSC (2000): Primary 12E10, 12E05; Secondary 13P05, 33C45
Published electronically: October 19, 2004
MathSciNet review: 2110427
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the resultants with respect to $x$ of certain linear forms in Chebyshev polynomials with argument $x$ are again linear forms in Chebyshev polynomials. Their coefficients and arguments are certain rational functions of the coefficients of the original forms. We apply this to establish several related results involving resultants and discriminants of polynomials, including certain self-reciprocal quadrinomials.


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Additional Information

Karl Dilcher
Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email: dilcher@mathstat.dal.ca

Kenneth B. Stolarsky
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: stolarsk@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03687-6
PII: S 0002-9947(04)03687-6
Keywords: Resultants, discriminants, Chebyshev polynomials, cyclotomic polynomials
Received by editor(s): November 1, 2002
Published electronically: October 19, 2004
Additional Notes: This research was supported in part by the Natural Sciences and Engineering Research Council of Canada
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.