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Resultants and discriminants of Chebyshev and related polynomials
Author(s):
Karl
Dilcher;
Kenneth
B.
Stolarsky
Journal:
Trans. Amer. Math. Soc.
357
(2005),
965-981.
MSC (2000):
Primary 12E10, 12E05;
Secondary 13P05, 33C45
Posted:
October 19, 2004
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Abstract:
We show that the resultants with respect to  of certain linear forms in Chebyshev polynomials with argument  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:
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
Posted:
October 19, 2004
Additional Notes:
This research was supported in part by the Natural Sciences and Engineering Research Council of Canada
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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