Thesis Abstract

This subject started with H. L. Montgomery’s famous paper [12], where he introduced a method to study the vertical distribution of the zeros of the Riemann zeta-function. Assuming the Riemann Hypothesis, he calculated the pair correlation of the zeros and from it deduced an estimate for the size of small gaps between the zeros and for the percentage of simple zeros. This paper opened a whole new …eld that later became a subject of major importance and has attracted lots of research interest. I apply Montgomery’s method to study the pair correlation of the zeros of ( (s); where ( (s) denotes the th derivative of Riemann’s xi-function. The function (s) has the same complex zeros as (s) and satis…es the functional equation (s) = (1 s). Since it is also entire, all its derivatives also satisfy a Riemann Hypothesis. Our main result is the following: