Roots of the derivative of the Riemann zeta function and of characteristic polynomials

E Duenez, DW Farmer, S Froehlich, C Hughes, F Mezzadri, T Phan

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)

Abstract

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 contributionRoots of the derivative of the Riemann zeta function and of characteristic polynomials
Original languageEnglish
Pages (from-to)2599 - 2621
Number of pages23
JournalNonlinearity
Volume23, number 10
DOIs
Publication statusPublished - Oct 2010

Bibliographical note

Publisher: IOP

Fingerprint Dive into the research topics of 'Roots of the derivative of the Riemann zeta function and of characteristic polynomials'. Together they form a unique fingerprint.

Cite this