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Periodic Orbits, Spectral Statistics, and the Riemann Zeros

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Supersymmetry and Trace Formulae

Part of the book series: NATO ASI Series ((NSSB,volume 370))

Abstract

My purpose in this article is to review the background to some recent developments in the semiclassical theory of spectral statistics. Specifically, I will concentrate on approaches based on the trace formula1,2; that is, on the link between quantum energy levels and classical periodic orbits. I will also review the closely related theory of the statistics of the zeros of the Riemann zeta function. My hope is to provide an introduction to the introductions of other papers in this volume on the same subjects, and with this in mind will discuss only in outline calculations to be described by them in greater detail.

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Author information

Authors and Affiliations

  1. School of Mathematics, University Walk, Bristol, BS8 1TW, UK

    J. P. Keating

  2. Hewlett-Packard Laboratories Bristol, Basic Research Institute in the Mathematical Sciences, Filton Road, Stoke Gifford, Bristol, BS 12 6QZ, UK

    J. P. Keating

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  1. J. P. Keating
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Editor information

Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Igor V. Lerner

  2. University of Bristol and Hewlett-Packard Laboratories, Bristol, UK

    Jonathan P. Keating

  3. University of Cambridge, Cambridge, UK

    David E. Khmelnitskii

  4. L. D. Landau Institute for Theoretical Physics, Moscow, Russia

    David E. Khmelnitskii

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Keating, J.P. (1999). Periodic Orbits, Spectral Statistics, and the Riemann Zeros. In: Lerner, I.V., Keating, J.P., Khmelnitskii, D.E. (eds) Supersymmetry and Trace Formulae. NATO ASI Series, vol 370. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4875-1_1

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  • DOI: https://doi.org/10.1007/978-1-4615-4875-1_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7212-7

  • Online ISBN: 978-1-4615-4875-1

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