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. © 2009 American Mathematical Society.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics