Automorphic forms on SL₂(R) / (Record no. 518378)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03397nam a22003618i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511896064 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160239.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 101123s1997||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511896064 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521580496 (hardback) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521072120 (paperback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA331 |
| Item number | .B687 1997 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.9 |
| Edition number | 21 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Borel, Armand, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Automorphic forms on SL₂(R) / |
| Statement of responsibility, etc | Armand Borel. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 1997. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (x, 192 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 130 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: -- 1. Prerequisites and notation -- 2. Review of SL2(R), differential operators, convolution -- 3. Action of G on X, discrete subgroups of G, fundamental domains -- 4. The unit disc model -- Part II. Automorphic Forms and Cusp Forms: -- 5. Growth conditions, automorphic forms -- 6. Poincare series -- 7. Constant term:the fundamental estimate -- 8. Finite dimensionality of the space of automorphic forms of a given type -- 9. Convolution operators on cuspidal functions -- Part III. Eisenstein Series: -- 10. Definition and convergence of Eisenstein series -- 11. Analytic continuation of the Eisenstein series -- 12. Eisenstein series and automorphic forms orthogonal to cusp forms -- Part IV. Spectral Decomposition and Representations: -- 13. Spectral decomposition of L2(G\G)m with respect to C -- 14. Generalities on representations of G -- 15. Representations of SL2(R) -- 16. Spectral decomposition of L2(G\SL2(R)): the discrete spectrum -- 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum -- 18. Concluding remarks. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Automorphic forms. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521580496 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 130. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511896064">https://doi.org/10.1017/CBO9780511896064</a> |
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