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Selberg formula for trace.

  1. May 23, 2007 #1


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    Could someone explain the 'Selberg Trace formula' concept??

    for example let be the Laplacian in curved Space-time:

    [tex] \Delta \Psi = E_{n} \Psi [/tex]

    My question is is there a relationship between the set of eigenvalues E(n) and a certain charasteristic of the SUrface (length, Areal or so on) due to Selberg Trace ?..thanks.
    Last edited: May 23, 2007
  2. jcsd
  3. May 24, 2007 #2

    Chris Hillman

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    Trace formula in a paragraph? I think not!

    Well, someone like Terry Tao can probably explain the gist in a paragraph, but I hardly dare try that myself. I'll say this much: it makes a big difference whether or not your manifold is compact and Riemannian.

    See survey articles like those in these books:

    Bert-Wolfgang Schulze and Hans Triebel (editors).
    Surveys on analysis, geometry, and mathematical physics.
    Teubner, 1990.

    Steven Zelditch
    Selberg trace formulae, and equidistribution theorems for closed geodesics and Laplace eigenfunctions : finite area surfaces
    American Mathematical Society, 1992

    Sources listed at
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