Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 2008 | Submitted
Journal Article Open

Zeta functions that hear the shape of a Riemann surface

Abstract

To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose "Riemannian" aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson-Sullivan measured. We prove that the ergodic rigidity theorem for this boundary action implies that the zeta functions of the spectral triple suffice to characterize the (anti-)complex isomorphism class of the corresponding Riemann surface. Thus, you can hear the complex analytic shape of a Riemann surface, by listening to a suitable spectral triple.

Additional Information

© 2008 Elsevier Ltd. Received 9 November 2007; revised 17 December 2007; accepted 30 December 2007. Available online 6 January 2008.

Attached Files

Submitted - 0708.0500.pdf

Files

0708.0500.pdf
Files (199.9 kB)
Name Size Download all
md5:b0c5b08c09db5068ce93c833560806d2
199.9 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
March 5, 2024