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On the zeta-functions of some simple Shimura varieties. (English) Zbl 0444.14016

MSC:
11G18 Arithmetic aspects of modular and Shimura varieties
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F72 Spectral theory; trace formulas (e.g., that of Selberg)
11R39 Langlands-Weil conjectures, nonabelian class field theory
11S37 Langlands-Weil conjectures, nonabelian class field theory
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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