Selberg Formula for Cofinite Groups and the Roelke Conjecture

TL;DR

This paper discusses the Selberg formula for cofinite groups and the Roelke conjecture but is withdrawn due to unresolved issues regarding the finiteness of a key quantity.

Contribution

The paper attempts to address the Selberg formula and Roelke conjecture for cofinite groups, though it remains incomplete and unverified.

Findings

The assertion about the finiteness of D_Γ is unproven for general groups.

The paper is withdrawn and does not present conclusive results.

The validity of the Roelke conjecture remains uncertain.

Abstract

The paper is withdrawn. The reviewer pointed out that the assertion that the quantity $D_{\Gamma}$ is finite (used by the author) is still unproved for the general group, and perhaps is false.