Some identities and congruences concerning Euler numbers and polynomials

In this paper, using the properties of the moments of p-adic measures, we establish some identities and Kummer likewise congruences concerning Euler numbers and polynomials. In the preliminaries, we introduce the Laplace transform which is an important tool for the determination of the moments of p-adic measures. We also give a sequence (d(n))(n), linked to Euler numbers and which satisfies the same type of congruences and identities as the Euler numbers. At the end, for p = 2, we give congruences on Euler numbers involving the sequence (d(n))(n). (C) 2010 Elsevier Inc. All rights reserved.