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Realisation de produits en couronne comme groupe de Galois de polynomes reciproques et construction de polynomes generiques

Franck Lalande (2002)

Acta Arithmetica

Reducibility and irreducibility of Stern $(0, 1)$ -polynomials

Karl Dilcher, Larry Ericksen (2014)

Communications in Mathematics

The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials $a (n; x)$ defined by $a (0; x) = 0$ , $a (1; x) = 1$ , $a (2 n; x) = a (n; x^{2})$ , and $a (2 n + 1; x) = x a (n; x^{2}) + a (n + 1; x^{2})$ ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that $a (n; x)$ can only have simple zeros, and we state a...

Displaying 1 – 16 of 16

Realisation de produits en couronne comme groupe de Galois de polynomes reciproques et construction de polynomes generiques

Reducibility and irreducibility of Stern $(0, 1)$ -polynomials

Reducibility of lacunary polynomials, IV

Reducibility of lacunary polynomials, V

Reducibility of lacunary polynomials, VI

Reducibility of Lacunary Polynomials, VII.

Reducibility of lacunary polynomials, VIII

Reducibility of lacunary polynomials. X

Reducibility of lacunary polynomials, XI

Reducibility of lacunary polynomials XII

Reducibility of polynomials of the form f(x)-g(y)

Reducibility of quadrinomials

Reducible lacunary polynomials

Relations between polynomial roots

Relations between polynomial roots

Résultats de stabilité algébrique.

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