Projects per year
We investigate the horizontal distribution of zeros of the derivative of the Riemann-zeta function and compare this with the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a surprising bimodal distribution which is yet to be explained. We show by example that the bimodality is a general phenomenon. For the unitary matrix case we prove a conjecture of Mezzadri concerning the leading order behaviour, and we show that the same follows from the random matrix conjectures for the zeros of the zeta function.
|Translated title of the contribution||Roots of the derivative of the Riemann zeta function and of characteristic polynomials|
|Pages (from-to)||2599 - 2621|
|Number of pages||23|
|Volume||23, number 10|
|Publication status||Published - Oct 2010|