Publication Date:
2014-07-17
Description:
The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann $\xi$ -function, $\xi (s)$ . Thus, if the Riemann hypothesis (RH) is true for the zeta-function, then it is true for $\xi (s)$ . Since $\xi (s)$ is entire, the zeros of $\xi '(s)$ , its derivative, would then also satisfy a Riemann hypothesis. We investigate the pair correlation function of the zeros of $\xi '(s)$ under the assumption that RH is true. We then deduce consequences about the size of gaps between these zeros and the proportion of these zeros that are simple.
Print ISSN:
0024-6107
Electronic ISSN:
1469-7750
Topics:
Mathematics
Permalink