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The arithmetic of consecutive polynomial sequences over finite fields

Abstract: Motivated by a question of van der Poorten about the existence of an infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen consecutively from a sequence in a finite field of odd prime characteristic. We study the arithmetic of such sequences, including bounds for the largest degree of irreducible factors, the number of irreducible factors, as well as for the number of such sequences of fixed length in which all the polynomials are irreducible.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Finite Fields and Their Applications 50 (2018) 35-65

Editorial: Elsevier

 Año de publicación: 2018

Nº de páginas: 31

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.ffa.2017.11.002

ISSN: 1071-5797,1090-2465

Proyecto español: MTM2014-55421-P