摘要：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 E n ∗ $E_{n}^{*}$ and the Dirichlet L-function L ( s , χ ) $L(s,i )$ . At the same time, we also prove a new congruence for the Euler numbers E n $E_{n}$ . That is, for any prime p ≡ 1 mod 8 $pquiv 1mod 8$ , we have E p − 3 2 ≡ 0 mod p $E_{ rac{p-3},}quiv 0mod p$ . As an application of our result, we give a new recursive formula for one kind of Dirichlet L-functions.
关键词：Euler numbers ; Euler numbers of the second kind ; Bernoulli polynomials ; Dirichlet L -function ; Identity ; Congruence
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