Commentarii Mathematici Helvetici


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Volume 78, Issue 4, 2003, pp. 731–739
DOI: 10.1007/s00014-003-0773-x

Published online: 2003-12-31

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

François Golse[1] and Pierre Lochak[2]

(1) École Polytechnique, Paris, France
(2) Paris, France

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.

Keywords: Riemann surfaces, Selberg trace formula, moduli spaces of curves

Golse François, Lochak Pierre: An infinitesimal trace formula for the Laplace operator on compact Riemann surfaces. Comment. Math. Helv. 78 (2003), 731-739. doi: 10.1007/s00014-003-0773-x