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Number theory --- 51 --- Mathematics --- L-functions. --- Representations of groups. --- 51 Mathematics

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This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.

Number theory --- Shimura varieties. --- L-functions. --- Functions, Zeta. --- Quaternions. --- Shimura varieties --- L-functions --- Functions, Zeta --- Quaternions --- Mathematical Theory --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Fonctions L. --- Fonctions zêta --- Functies L. --- Functions [Zeta ] --- Funsties [Zêta ] --- Shimura variëteiten --- Variétés de Shimura --- Zeta functions --- Zêta functies --- Number theory. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Varieties, Shimura --- Arithmetical algebraic geometry

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Number theory --- L-functions --- Representations of groups --- 517.547.5 --- Automorphic forms --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Automorphic functions --- Forms (Mathematics) --- Functions, L --- -Number theory --- Special classes of analytic functions. Algebraic and algebroid functions. Automorphic functions --- Automorphic forms. --- L-functions. --- Representations of groups. --- 517.547.5 Special classes of analytic functions. Algebraic and algebroid functions. Automorphic functions --- -517.547.5 Special classes of analytic functions. Algebraic and algebroid functions. Automorphic functions