ON ALGEBRAIC INTEGERS WHICH ARE 2-SALEM ELEMENTS IN POSITIVE CHARACTERISTIC

Sur les Entiers Algébriques qui sont des Eléments 2-Salem en Caractéristique Positive

Mabrouk Ben Nasr (1) , Hassen Kthiri (1) , Jean-Louis Verger-Gaugry (2)

1 Université de Sfax - University of Sfax
2 LAMA - Laboratoire de Mathématiques

Bateman and Duquette have initiated the study of Salem elements in positive characteristic. This work extends their results to 2-Salem elements whose minimal polynomials are of the type Y^n + λ_(n−1) Y^(n−1) +. .. + λ_1 Y + λ_0 ∈ F_q [X][Y ] where n ≥ 2, λ_0 \neq 0 and deg λ_(n−1) < deg λ_(n−2) = max_{i \neq n−2} deg λ_i. This work provides an analogue of their results for 2-Salem elements whose minimal polynomials meet certain requirements.

Mots clés: Finite field; Laurent series; 2-Salem series; 2-Salem element; irreducible polynomial; Newton polygon; Salem element; Salem number; Finite field; Salem element.; 11R06; 11R09; 11R52; 12D10

Domaines: Théorie des nombres [math.NT]

Mabrouk Ben Nasr, Hassen Kthiri, Jean-Louis Verger-Gaugry. ON ALGEBRAIC INTEGERS WHICH ARE 2-SALEM ELEMENTS IN POSITIVE CHARACTERISTIC. 2020. ⟨hal-03090505⟩