| Description |
1 online resource (xi, 324 pages) : illustrations |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 311-319) and index. |
| Contents |
Lifting autonomic forms of PGSp(2) to PGL(4) -- Zeta functions of Shimura varieties of PGSp(2) -- Background. |
| Summary |
The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings." This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,) in SL(4,). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Automorphic forms.
|
|
Automorphic forms. |
|
Shimura varieties.
|
|
Shimura varieties. |
|
Symplectic groups.
|
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Symplectic groups. |
|
Functions, Zeta.
|
|
Functions, Zeta. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Flicker, Yuval Z. (Yuval Zvi), 1955- Automorphic forms and Shimura varieties of PGSp (2). Singapore ; US Office, Hackensack, NJ : World Scientific Pub., ©2005 9812564039 (DLC) 2006274952 (OCoLC)70107204 |
| ISBN |
9812703322 (electronic book) |
|
9789812703323 (electronic book) |
|
1281899267 |
|
9781281899262 |
|
