MULTINOMIAL COEFFICIENTS, MULTIPLE ZETA VALUES, EULER SUMS AND SERIES OF POWERS OF THE HURWITZ ZETA FUNCTION

We generalize Chen's theorem [2] Sigma(m)(r=1)Sigma(vertical bar alpha vertical bar=m) (m alpha) zeta(alpha n) = zeta(m)(n) for complex arguments, presenting a very elementary proof. Subsequently, using a similar technique, we obtain a general formula that allows us to prove relations between nonlinear Euler sums. We also present relations between series of powers of the Hurwitz zeta function and the multiple zeta function, like Sigma(infinity)(n=1) zeta(m)(H)(s, n) = Sigma(m)(r=1)Sigma(vertical bar alpha vertical bar=m) (m alpha) zeta(alpha(1)s - 1, alpha(2)s,..., alpha(r)s).