LAUSR

The aim of this paper is using an elementary method and the properties of the Bernoulli polynomials to establish a close relationship between the Euler numbers of the second kind En∗$E_{n}^{*}$ and the Dirichlet L-function L(s,χ)$L(s,\chi )$. At the same time, we also prove a new congruence for the Euler numbers En$E_{n}$. That is, for any prime p≡1mod8$p\equiv 1\bmod 8$, we have Ep−32≡0modp$E_{\frac{p-3}{2}}\equiv 0\bmod p$. As an application of our result, we give a new recursive formula for one kind of Dirichlet L-functions.