Irreducible factorization of translates of reversed Dickson polynomials over finite fields

Evans Ron; Van Veen Mark

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Irreducible factorization of translates of reversed Dickson polynomials over finite fields

机译：有限域上逆Dickson多项式的平移的不可约分解

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摘要

Let F-q be a field of q elements, where q is a power of an odd prime. Fix n = (q + 1)/2. For each s is an element of F-q, we describe all the irreducible factors over F q of the polynomial g(s)(y) := y(n) + (1 - y)(n) - s, and we give a necessary and sufficient condition on s for g(s)(y) to be irreducible. (C) 2018 Elsevier Inc. All rights reserved.

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《Finite fields and their applications》 |2018年第11期|151-175|共25页
作者
Evans Ron; Van Veen Mark;
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作者单位

Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA;

Varasco LLC, 2138 Edinburg Ave, Cardiff By The Sea, CA 92007 USA;

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正文语种 eng
中图分类
关键词
Reversed Dickson polynomials over finite fields; Irreducible factorization of polynomials; Second order linear recurring sequence; Quadratic residuacity;

机译：有限域上的逆Dickson多项式;多项式的不可约分解;二阶线性递归序列;二次残基;

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1. Explicit factorizations of generalized Dickson polynomials of order 2(m) via generalized cyclotomic polynomials over finite fields [J] . Tosun Cemile Finite fields and their applications . 2016,第Mara期

机译：通过有限域上的广义环原子多项式对阶数为2（m）的广义Dickson多项式进行显式分解
2. The first and second moments of reversed Dickson polynomials over finite fields [J] . Cheng Kaimin, Hong Shaofang Journal of Number Theory . 2018,第期

机译：在有限领域逆转迪克逊多项式的第一矩和第二次
3. Permutational behavior of reversed Dickson polynomials over finite fields [J] . Kaimin Cheng AIMS Mathematics . 2017,第2期

机译：逆Dickson多项式在有限域上的置换行为。
4. Explicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields [C] . Robert W. Fitzgerald, Joseph L. Yucas International Workshop on Arithmetic of Finite Fields(WAIFI 2007); 200706; Madrid(ES) . 2007

机译：有限域上环原子和Dickson多项式的显式分解
5. On the Existence of Irreducible Polynomials with Prescribed Coefficients over Finite Fields. [D] . Tzanakis, Georgios. 2010

机译：有限域上具有规定系数的不可约多项式的存在性。
6. Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials [O] . Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, -1

机译：第二类Chebyshev多项式和Fibonacci多项式的有限积的和
7. Irreducible factorization of translates of reversed Dickson polynomials over finite fields [O] . Ron Evans, Mark Van Veen 2018

机译：有限田逆转迪克森多项式转化的不可减少分解

Irreducible factorization of translates of reversed Dickson polynomials over finite fields

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