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.
On the span of polynomials with integer coefficients / Capparelli, Stefano; DEL FRA, Alberto; Carlo, Scio. - In: MATHEMATICS OF COMPUTATION. - ISSN 0025-5718. - STAMPA. - 79:270(2010), pp. 967-981. [10.1090/s0025-5718-09-02292-3]
On the span of polynomials with integer coefficients
CAPPARELLI, Stefano;DEL FRA, ALBERTO;
2010
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
