The Pair correlation of zeros of derivatives of Riemann's xi-function

Thesis (Ph. D.)--University of Rochester. Dept. of Mathematics, 2008.In this thesis, we apply Montgomery’s method to study the pair correlation function of the zeros of ξ(κ)(s), the κth derivative of Riemann’s xi-function. Our work suggests that the zeros tend to even out when we take high derivatives, a fact predicted by a general theorem of Farmer and Rhoades. We explore this and also obtain new results on the size of small gaps between the zeros of ξ(κ)(s) and on the percentage of simple zeros of ξ(κ)(s)