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Pré-Publication, Document De Travail Année : 2020

On 2-Salem polynomials and 2-Salem numbers in positive characteristic

Résumé

Bateman and Duquette have characterized Salem numbers in positive characteristic. This work extends their results to 2-Salem numbers from 2-Salem minimal polynomials of the type Y n + λn−1Y n−1 +. .. + λ1Y + λ0 ∈ Fq[X][Y ] where n ≥ 2, λ0 = 0 and deg λn−1 < deg λn−2 = sup i =n−2 deg(λi). The existence of 2-Salem polynomials over Fq, and related questions of irreducibility and algebraicity of 2-Salem numbers, are studied by means of Weiss's method of upper Newton polygons, for q = 2 r , r ≥ 1.
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Dates et versions

hal-02464774 , version 1 (03-02-2020)

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  • HAL Id : hal-02464774 , version 1

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Mabrouk Ben Nasr, Hassen Kthiri, Jean-Louis Verger-Gaugry. On 2-Salem polynomials and 2-Salem numbers in positive characteristic. 2020. ⟨hal-02464774⟩
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