Zeta functions and the trace formula

  • Werner Hoffmann

    Universität Bielefeld, Germany
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Prehomogeneous vector spaces provide a framework for the method of analytic continuation of zeta integrals due to Hecke and Tate. We will describe instances where convergence can only be achieved by truncation. Special values of such zeta integrals appear in the Arthur–Selberg trace formula, and their study is relevant in connection with recent ideas in the Langlands program.