On nth order Euler polynomials of degree n that are Eisenstein

被引：1
|
作者：
Filaseta, Michael [1 ]
Luckner, Thomas [2 ]
机构：
[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA
[2] Flagler Coll, Dept Math, St Augustine, FL 32084 USA
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2024年 / 35卷 / 01期
关键词：
Bernoulli number; Eisenstein polynomial; Euler polynomial; Genoocchi number; Irreducible polynomial; GENOCCHI NUMBERS; CONGRUENCES;
D O I：
10.1016/j.indag.2023.09.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For m an even positive integer and p an odd prime, we show that the generalized Euler polynomial mp (x) is in Eisenstein form with respect to p if and only if p does not divide m(2m - 1)Bm. As a consequence, we deduce that at least 1/3 of the generalized Euler polynomials En(n)(x) are in Eisenstein form with respect to a prime p dividing n and, hence, irreducible over Q. (c) 2023 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
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页码：76 / 86
页数：11
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