On some averages at the zeros of the derivatives of the Riemann zeta-function

In this article we study two problems raised by a work of Conrey and Ghosh from 1989. Let zeta((k))(s) be the k-th derivative of the Riemann zeta-function, and chi(s) be factor in the functional equation of the Riemann zeta-function. We calculate the average values of zeta((j)) and chi at the nontrivial zeros of zeta((k)). (C) 2011 Elsevier Inc. All rights reserved.