Small Eigenvalues

Part of the Modern Birkhäuser Classics book series (MBC)


The asymptotic length distribution of the closed geodesics on a compact Riemann surface S is strongly influenced by the eigenvalues of the Laplacian in the interval [0,1/4].In the prime number theorem (Theorem 9.6.1) and in many applications of Selberg’s trace formula, the distinction between eigenvalues above and eigenvalues below 1/4 is essentially for technical reasons and has to do with the fact.


Riemann Surface Small Eigenvalue Compact Riemann Surface Piecewise Smooth Boundary Geodesic Triangle 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Département de MathématiquesEcole Polytechnique Fédérale de LausanneLausanne-EcublensSwitzerland

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