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On the span of polynomials with integer coefficients


Authors: Stefano Capparelli, Alberto Del Fra and Carlo Sciò
Journal: Math. Comp. 79 (2010), 967-981
MSC (2000): Primary 12D10; Secondary 30C15, 11C08
DOI: https://doi.org/10.1090/S0025-5718-09-02292-3
Published electronically: September 8, 2009
MathSciNet review: 2600551
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Abstract | References | Similar Articles | Additional Information

Abstract: Following a paper of R. Robinson, we classify all hyperbolic polynomials in one variable with integer coefficients and span less than 4 up to degree 14, and with some additional hypotheses, up to degree 17. We conjecture that the classification is also complete for degrees 15, 16, and 17.

Besides improving on the method used by Robinson, we develop new techniques that turn out to be of some interest.

A close inspection of the polynomials thus obtained shows some properties deserving further investigations.


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Additional Information

Stefano Capparelli
Affiliation: Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma “La Sapienza”, Via Scarpa 16, I-00161 Roma, Italy
Email: capparelli@dmmm.uniroma1.it

Alberto Del Fra
Affiliation: Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma “La Sapienza”, Via Scarpa 16, I-00161 Roma, Italy
Email: alberto.delfra@uniroma1.it

Carlo Sciò
Affiliation: ENEA FIM, Via E. Fermi 45, I-00044 Frascati (RM), Italy
Email: scio@frascati.enea.it

DOI: https://doi.org/10.1090/S0025-5718-09-02292-3
Received by editor(s): November 10, 2008
Received by editor(s) in revised form: April 4, 2009
Published electronically: September 8, 2009
Article copyright: © Copyright 2009 American Mathematical Society