An Arithmetic Invariant of the Jacquet-Langlands correspondence
Abstract
We describe the local-global compatibility of local Plancherel measures and the Tamagawa measure under the Jacquet-Langlands correspondence. We apply the notion of densities of modules over a discrete group, which generalizes the dimensions over a discrete group. We prove that the global Jacquet-Langlands correspondence preserves the densities over principal arithmetic groups.
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