Selberg trace formula
= Selberg trace formula
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For a compact <hyperbolic surface>, the Selberg trace formula equates a sum over <Laplace-Beltrami operator> <eigenvalues> to an area term and a sum over primitive closed <geodesics> and their iterates. It proves that the <Laplacian> <spectrum> and the unmarked <length spectrum>, with multiplicities, determine each other.