The arithmetic of consecutive polynomial sequences over finite fields

Domingo Gómez-Pérez, Alina Ostafe, Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)35-65
Number of pages31
JournalFinite Fields and their Applications
Volume50
DOIs
Publication statusPublished - 1 Mar 2018
Externally publishedYes

Keywords

  • Character sum
  • Consecutive irreducible sequence
  • Consecutive polynomial sequence

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