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## 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 contribution | Roots of the derivative of the Riemann zeta function and of characteristic polynomials |
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Original language | English |

Pages (from-to) | 2599 - 2621 |

Number of pages | 23 |

Journal | Nonlinearity |

Volume | 23, number 10 |

DOIs | |

Publication status | Published - 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.

## Projects

- 1 Finished