Bernoulli and poly-Bernoulli polynomial convolutions and identities of p-adic Arakawa-Kaneko zeta functions

摘要

We evaluate the ordinary convolution of Bernoulli polynomials in closed form in terms of poly-Bernoulli polynomials. As applications we derive identities for p-adic Arakawa-Kaneko zeta functions, including a p-adic analogue of Ohno's sum formula. These p-adic identities serve to illustrate the relationships between real periods and their p-adic analogues.