Oct. 22, 2019 Tuesday 15:00pm

Speaker:Yoonbok Lee (Incheon National University)

Title: Pair correlation of the zeros of the derivative of the Riemann ξ-function

Abstract:

The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann

ξ-function, ξ(s). Thus, if the Riemann hypothesis (RH) is true for the zeta-function, then it

is true for ξ(s). Since ξ(s) is entire, the zeros of ξ(s), its derivative, would then also satisfy a Riemann hypothesis. We investigate the pair correlation function of the zeros of ξ(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.

Speaker:Yoonbok Lee (Incheon National University)

Title: Pair correlation of the zeros of the derivative of the Riemann ξ-function

Abstract:

The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann

ξ-function, ξ(s). Thus, if the Riemann hypothesis (RH) is true for the zeta-function, then it

is true for ξ(s). Since ξ(s) is entire, the zeros of ξ(s), its derivative, would then also satisfy a Riemann hypothesis. We investigate the pair correlation function of the zeros of ξ(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.