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Asymptotic distributions on super-Riemann surfaces

The Selberg supertrace formula for super-Riemann surfaces is used to derive asymptotic distributions for the number of eigenvalues of the Dirac - Laplace operator on super-Riemann surfaces, and for the number of the norms N of the hyperbolic conjugacy classes. In the case where the underlying Riemann surface is compact, we find that the Witten index is determined by the area of the Riemann surface.