An Introduction to Automorphic Representations (Record no. 58060)
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| fixed length control field | 05094nam a22005895i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-41153-3 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030111457.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
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| fixed length control field | 240301s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031411533 |
| -- | 978-3-031-41153-3 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-41153-3 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA241-247.5 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBH |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT022000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBH |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Getz, Jayce R. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 72297 |
| 245 13 - TITLE STATEMENT | |
| Title | An Introduction to Automorphic Representations |
| Medium | [electronic resource] : |
| Remainder of title | With a view toward trace formulae / |
| Statement of responsibility, etc. | by Jayce R. Getz, Heekyoung Hahn. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer International Publishing : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XVIII, 609 p. 1 illus. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Graduate Texts in Mathematics, |
| International Standard Serial Number | 2197-5612 ; |
| Volume/sequential designation | 300 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Affine Algebraic Groups -- 2. Adeles -- 3. Discrete Automorphic Representations -- 4. Archimedean Representation Theory -- 5. Representations of Totally Disconnected Groups -- 6. Automorphic Forms -- 7. Unramified Representations -- 8. Nonarchimedean Representation Theory -- 9. The Cuspidal Spectrum -- 10. Einsenstein Series -- 11. Rankin-Selberg L-functions -- 12. Langlands Functoriality -- 13. Known Cases of Global Langlands Functoriality -- 14. Distinction and Period Integrals -- 15. The Cohomology of Locally Symmetric Spaces -- 16. Spectral Sides of the Trace Formulae -- 17. Orbital Integrals -- 18. Simple Trace Formulae -- 19. Applications of Trace Formulae -- A. Groups attached to involutions of algebras -- B. The Iwasawa Decomposition -- C. Poisson Summation -- D. Alternate conventions related to adelic quotients -- Hints to selected exercises -- References -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics. The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed. This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 9 (RLIN) | 72298 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 9 (RLIN) | 72302 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72303 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72304 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72305 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 72306 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Hahn, Heekyoung. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 72307 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031411519 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031411526 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031426100 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Graduate Texts in Mathematics, |
| International Standard Serial Number | 2197-5612 ; |
| Volume number/sequential designation | 300 |
| 9 (RLIN) | 72308 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-41153-3">https://doi.org/10.1007/978-3-031-41153-3</a> |
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