Selberg Formula for Cofinite Groups and the Roelke Conjecture

Abstract

As the reviewer have pointed out, the proof of Roelke Conjecture contains an error. For cofinite groups, we obtain a formula connecting the discrete spectrum of Laplace operator and the resonance spectrum. Using this formula, we give a proof of the Roelke conjecture. In this version, we make several corrections in Theorem 1 and Lemma 5.