Can one hear the Riemann zeros in black hole ringing?

Rodrigo Aros, Fabrizzio Bugini, Danilo E. Diaz

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


We elaborate on an entry of the AdS/CFT dictionary relating functional determinants: the determinant of the one-loop contribution to the effective gravitational action by bulk scalars in an asymptotically locally AdS background X, and the determinant of the two-point function of the dual operator (a.k.a. scattering matrix) at the conformal boundary M. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk gravitational partition function to a subleading large-N contribution in the boundary CFT partition function: The formula applies to quotients of AdS as well [1]. In the particular case of the BTZ black hole, a closed expression can be worked out in terms of an associated Patterson-Selberg zeta function ZBTZ (λ) [2]. The determinants can then be thought of as regularized products of either zeta zeros, scattering resonances or quasinormal frequencies [3]. In this sense, one could say that the zeros of ZBTZ (λ) can be heard in the spectrum of quasinormal modes of the BTZ black hole. The question we want to pose is whether a similar situation might exist for the celebrated zeros of the Riemann zeta function.

Original languageEnglish
Article number012009
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 2016
Event19th Chilean Physics Symposium 2014 - Concepcion, Chile
Duration: 26 Nov 201428 Nov 2014

ASJC Scopus subject areas

  • General Physics and Astronomy


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