JournalscmhVol. 78, No. 4pp. 731–739

An infinitesimal trace formula for the Laplace operator on compact Riemann surfaces

  • François Golse

    École Polytechnique, Paris, France
  • Pierre Lochak

    Paris, France
An infinitesimal trace formula for the Laplace operator on compact Riemann surfaces cover
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Abstract

We derive an infinitesimal (or variational) version of the Selberg trace formula for compact Riemann surfaces, which gives information on the behaviour of the eigenvalues of the Laplace-Beltrami operator as the surface varies over the appropriate moduli space.

Cite this article

François Golse, Pierre Lochak, An infinitesimal trace formula for the Laplace operator on compact Riemann surfaces. Comment. Math. Helv. 78 (2003), no. 4, pp. 731–739

DOI 10.1007/S00014-003-0773-X