On the parity of poly-Euler numbers. (English) Zbl 1334.11014
Summary: Poly-Euler numbers are introduced in [Y. Sasaki, J. Number Theory 132, No. 1, 156–170 (2012; Zbl 1268.11135)] via special values of an \(L\)-function as a generalization of the Euler numbers. In this article, poly-Euler numbers with negative index are mainly treated, and the parity of them is shown as the main theorem. Furthermore the divisibility of poly-Euler numbers are also discussed.
MSC:
11B68 | Bernoulli and Euler numbers and polynomials |
11M41 | Other Dirichlet series and zeta functions |