The house of an algebraic integer all of whose conjugates lie in a sectorReportar como inadecuado




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1 Analyse IECL - Institut Élie Cartan de Lorraine

Abstract : Let α be a nonzero algebraic integer of degree d, all of whose conjugates α i lie in a sector | arg z| ≤ θ, 0 ≤ θ < π. The house of α is the largest modulus of its conjugates. We treat here the notion of house using the method of explicit auxiliary functions. This work seems to be the first of this kind. For 0 < θ < π, we compute the greatest lower bound hθ of the house of all such α, for θ belonging to nine subintervals of 0, π. Moreover, among these subintervals, six are consecutive and complete. The polynomials involved in the auxiliary functions are found by our recursive algorithm.





Autor: V Flammang -

Fuente: https://hal.archives-ouvertes.fr/



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