By the same authors

From the same journal

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

Research output: Contribution to journalArticle

Author(s)

  • Eduardo Duenez
  • David W. Farmer
  • Sara Froehlich
  • C. P. Hughes
  • Francesco Mezzadri
  • Toan Phan

Department/unit(s)

Publication details

JournalNonlinearity
DatePublished - Oct 2010
Issue number10
Volume23
Number of pages23
Pages (from-to)2599-2621
Original languageEnglish

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.

    Research areas

  • CRITICAL LINE, ZEROS

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations