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.

引用

页码：76 / 86

页数：11

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