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On the span of polynomials with integer coefficients. (English) Zbl 1216.12001

Summary: Following a paper of R. M. Robinson [Math. Comput. 18, 547–559 (1964; Zbl 0147.12905)], 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.

MSC:

12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
11C08 Polynomials in number theory

Citations:

Zbl 0147.12905
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References:

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