$p$-adic Congruencens of Generalized Euler Numbers and Relations to Even Zeta Value
Number Theory
2026-05-12 v1
Abstract
In this article, we introduce congruential Euler numbers, which are a further generalization of generalized Euler numbers. We prove the -adic congruences of congruential Euler numbers, which include answers to a conjecture related to Lehmer numbers. We also provide expressions of even zeta values using congruential Euler numbers via complex analysis.
Cite
@article{arxiv.2605.10677,
title = {$p$-adic Congruencens of Generalized Euler Numbers and Relations to Even Zeta Value},
author = {Yuta Nishibuchi},
journal= {arXiv preprint arXiv:2605.10677},
year = {2026}
}
Comments
21 pages, 2 tables