The arithmetic of consecutive polynomial sequences over finite fields

被引：3

作者：

Gomez-Perez, Domingo ^{[1
]}

Ostafe, Alina ^{[2
]}

Sha, Min ^{[2
]}

机构：

[1] Univ Cantabria, Dept Math Stat & Comp Sci, Santander 39005, Spain

[2] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2018年 / 50卷

基金：

澳大利亚研究理事会;

关键词：

Consecutive polynomial sequence; Consecutive irreducible sequence; Character sum; IRREDUCIBLE POLYNOMIALS; PRIMITIVE DIVISORS;

D O I：

10.1016/j.ffa.2017.11.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：35 / 65

页数：31

共 34 条

[1]

ANGELL IO, 1977, MATH COMPUT, V31, P265, DOI 10.1090/S0025-5718-1977-0427213-2

[2]

[Anonymous], 1995, ACTA SCI MATH

[3]

[Anonymous], LONDON MATH SOC LECT

[4]

[Anonymous], MATH INTELL

[5]

[Anonymous], VERH 1 INT MATH K

[6]

[Anonymous], EXP MATH

[7]

[Anonymous], CONCRETE INTRO HIGHE

[8]

Bilu Y, 2001, J REINE ANGEW MATH, V539, P75

[9] Polynomial distribution and sequences of irreducible polynomials over finite fields [J].

Chou, WS ;

Cohen, SD .

JOURNAL OF NUMBER THEORY, 1999, 75 (01) :145-159

[10]

Euler L., 1738, Commentarii academiae scientiarum Petropolitanae, P216

← 1 2 3 4 →