| Abstract:
Given a finite volume hyperbolic n-manifold $M$ with totally
geodesic boundary, an orthogeodesic of $M$ is a geodesic arc which is
perpendicular to the boundary. For each dimension n, we show there is a
real valued function $F_n$ such that the volume of any $M$ is the sum of
values of $F_n$ on the orthospectrum (length of orthogeodesics). For $n=2$
the function $F_2$ is the Rogers L-function and the summation identities
give dilogarithm identities on the Moduli space of surfaces.
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