The Arithmetic of Consecutive Polynomial Sequences over Finite Fields

Domingo Gómez-Pérez; Alina Ostafe; Min Sha

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arXiv · 1509.01936

The Arithmetic of Consecutive Polynomial Sequences over Finite Fields

Domingo Gómez-Pérez·Alina Ostafe·Min Sha

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Abstract

Motivated by a question of van der Poorten about the existence of 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.

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BibTeX RIS

Domingo Gómez-Pérez, Alina Ostafe, Min Sha. 2018-05-23. The Arithmetic of Consecutive Polynomial Sequences over Finite Fields. https://arxiv.org/abs/1509.01936

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