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The semi-simple zeta function of quaternionic Shimura varieties / Harry Reimann.

By: Reimann, Harry, 1956-Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1657.Publication details: Berlin ; New York : Springer, ©1997. Description: 1 online resource (143 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540684145; 354068414XSubject(s): Shimura varieties | L-functions | Functions, Zeta | Quaternions | Variétés de Shimura | Fonctions L | Fonctions zêta | Quaternions | Functions, Zeta | L-functions | Quaternions | Shimura varieties | Zetafunktion | Divisionsalgebra | Quaternion | Shimura-Mannigfaltigkeit | Shimura variëteiten | Teoria dos numeros | Algebra associativa | Fonctions LGenre/Form: Electronic books. Additional physical formats: Print version:: Semi-simple zeta function of quaternionic Shimura varieties.DDC classification: 510 s | 512/.74 LOC classification: QA3 | .L28 no. 1657Other classification: 31.14 | SI 850 | SK 180 | SK 240 | MAT 302f | MAT 146f Online resources: Click here to access online Summary: 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.
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Includes bibliographical references (pages 136-139) and index.

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.

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