Congruence properties of Lehmer-Euler numbers

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2025-01-10 DOI:10.1007/s00010-024-01150-5

Takao Komatsu, Guo-Dong Liu

引用次数: 0

Abstract

Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer’s generalized Euler numbers are studied to give certain congruence properties together with recurrence and explicit formulas of the numbers. We also show a new polynomial sequence and its properties. Some identities including Euler and central factorial numbers are obtained.

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Lehmer-Euler数的同余性质

Lehmer在1935年用单位的三次方根定义了欧拉数的某种推广，作为伯努利数和欧拉数的自然推广。本文研究了Lehmer广义欧拉数，给出了若干同余性质，并给出了这些数的递归式和显式公式。我们还给出了一个新的多项式序列及其性质。得到了欧拉数和中心阶乘数等恒等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.