a1 Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A.
The purpose of this paper is to take some first steps the investigation of the negative moments
where k>0 and 12, and the related discrete moments
where runs over the complex zeros of the zeta-function. We assume the Riemann hypothesis (RH) throughout; it then follows that Ik(, T) converges for every k > 0 when > but for no k = when =. We further note that Jk(T) is only defined for all T if all the zeros are simple and, in that case, Ik(, T) converges for all k<.
(Received July 26 1988)