Congruence properties of Lehmer-Euler numbers
Number Theory
2025-01-03 v1 Combinatorics
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.
Cite
@article{arxiv.2501.01178,
title = {Congruence properties of Lehmer-Euler numbers},
author = {Takao Komatsu and Guo-Dong Liu},
journal= {arXiv preprint arXiv:2501.01178},
year = {2025}
}