Newton and Schinzel sequences in quadratic fields

David Adam; Paul-Jean Cahen

doi:10.5802/acirm.28

David Adam ¹; Paul-Jean Cahen ²

¹ GAATI, Université de Polynésie Française, BP 6570, 98702 Faa’a, Tahiti, Polynésie Française
² LATP, CNRS UMR 6632, Faculté des Sciences et Techniques, Université d’Aix-Marseille III, 13397 Marseille Cedex 20, France

Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 15-20.

Abstract

We give the maximal length of a Newton or a Schinzel sequence in a quadratic extension of a global field. In the case of a number field, the maximal length of a Schinzel sequence is 1, except in seven particular cases, and the Newton sequences are also finite, except for at most finitely many cases, all real. We give the maximal length of these sequences in the special cases. We have similar results in the case of a quadratic extension of a function field $𝔽_{q} (T)$ , taking in account that the ring of integers may be isomorphic to $𝔽_{q} [T]$ , in which case there are obviously infinite Newton and Schinzel sequences.

Published online: 2011-10-19

Zbl: 06938576

DOI: 10.5802/acirm.28

Classification: 13F20, 11R58
Keywords: Integer-valued polynomials, Newton and Schinzel sequences, Quadratic number and function fields

Author's affiliations:

David Adam ¹; Paul-Jean Cahen ²

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David Adam; Paul-Jean Cahen. Newton and Schinzel sequences in quadratic fields. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 15-20. doi : 10.5802/acirm.28. https://acirm.centre-mersenne.org/articles/10.5802/acirm.28/

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