I've been reading the paper "LARGE SPACES BETWEEN THE ZEROS OF THE RIEMANN ZETA-FUNCTION" by S. H. Saker (arXiv-0906.5458v3 [math.NT]). http://arxiv.org/abs/0906.5458. The author employs conjectures on the moments of $\zeta(s)$ and $\zeta'(s)$ to derive bounds on the average spacing $\Lambda(k)$ between the zeros of $\zeta(s)$ on the critical line. Here $k$ refers to the order of the moment under consideration.

My question is this: what does it mean for the spacing to depend upon $k$? I'm sure I'm missing the point. I thought that there would be bounds that did not depend upon any parameter.

Thanks, Tom