Geometric zeta functions of higher rank and the invariant trace formula

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The theory of geometric zeta functions shall be extended to the case of non-compact locally symmetric spaces of higher rank. The real and the p-adic case shall be treated simultaneously. The ensuing zeta functions are functions of severel variables, which encode not only lengthes of closed geodesics, but also their relative position in the symmetric space or building. In the case of arithmetic quotients, number theoretic applications are possible, like asymptotic assertions about class numbers.