Shintani zeta functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1993
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| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society lecture note series
183 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 339 S. |
| ISBN: | 0521448042 |
Staff View
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| 100 | 1 | |a Yukie, Akihiko |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Shintani zeta functions |c Akihiko Yukie |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1993 | |
| 300 | |a XII, 339 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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Table of contents
Preface
Notation
Introduction
§0.1 What is a prehomogeneous vector space?
§0.2 The classification
§0.3 The global zeta function
§0.4 The orbit space Gk \ Vfcss
§0.5 The filtering process and the local theory: a note by D. Wright
§0.6 The outline of the general procedure
Part I The general theory
Chapter 1 Preliminaries
§1.1 An invariant measure on GL(n)
§1.2 Some adelic analysis
Chapter 2 Eisenstein series on GL(n)
§2.1 The Fourier expansion of automorphic forms on GL(n)
§2.2 The constant terms of Eisenstein series on GL(n)
§2.3 The Whittaker functions
§2.4 The Fourier expansion of Eisenstein series on GL(n)
Chapter 3 The general program
§3.1 The zeta function
§3.2 The Morse stratification
§3.3 The paths
§3.4 Shintani's lemma for GL(n)
§3.5 The general process
§3.6 The passing principle
§3.7 Wright's principle
§3.8 Examples
Part II The Siegel Shintani case
Chapter 4 The zeta function for the space of quadratic forms
§4.1 The space of quadratic forms
§4.2 The case n = 2
§4.3 /3 sequences
§4.4 An inductive formulation
§4.5 Paths in Pi
§4.6 Paths in fp3, p4
§4.7 The cancellations
§4.8 The work of Siegel and Shintani
Part III Preliminaries for the quartic case
Chapter 5 The case G = GL(2) x GL(2), V = Sym2*2 ® k2
§5.1 The space Sym2fc2 ® k2
§5.2 The adjusting term
§5.3 Contributions from 0i,i 3
§5.4 Contributions from £ 2, 4
§5.5 The contribution from V™k
§5.6 The principal part formula
viii Table of Contents
Chapter 6 The case G = GL(2) x GL(1)2, V = Sym2*:2 © k
§6.1 Reducible prehomogeneous vector spaces with two irreducible factors
§6.2 The spaces Syrn2*;2 © k, Sym2k2 © k2
§6.3 The principal part formula
Chapter 7 The case G = GL(2) x GL(1)2, V = Sym2k2 © k2
§7.1 Unstable distributions
§7.2 Contributions from unstable strata
§7.3 The principal part formula
Part IV The quartic case
Chapter 8 Invariant theory of pairs of ternary quadratic forms
§8.1 The space of pairs of ternary quadratic forms
§8.2 The Morse stratification
§8.3 /3 sequences of lengths 2
Chapter 9 Preliminary estimates
§9.1 Distributions associated with paths
§9.2 The smoothed Eisenstein series
Chapter 10 The non constant terms associated with unstable strata
§10.1 The case 0 = (ft)
§10.2 The cases t) = (ft), (fto, fto.i)
§10.3 The cases 0 = (ft), (ft, Am)
§10.4 The case 0 = (ft)
§10.5 The case 0 = (ft)
§10.6 The cases 0 = (ft, ft,2), (ft)
Chapter 11 Unstable distributions
§11.1 Unstable distributions
§11.2 Technical lemmas
Chapter 12 Contributions from unstable strata
§12.1 The case 0 = (ft)
§12.2 The case E = (ft)
§12.3 The case 0 = (ft)
§12.4 The case 0 = (ft)
§12.5 The case 0 = (ft)
§12.6 The case 0 = (ft)
§12.7 The case 0 = (ft)
§12.8 The case 3 = (ft)
§12.9 The case 0 = (ft)
§12.10 The case 0 = (/3W)
Chapter 13 The main theorem
§13.1 The cancellations of distributions
§13.2 The principal part formula
§13.3 Concluding remarks
Bibliography
List of symbols
Index |
| any_adam_object | 1 |
| author | Yukie, Akihiko |
| author_facet | Yukie, Akihiko |
| author_role | aut |
| author_sort | Yukie, Akihiko |
| author_variant | a y ay |
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| bvnumber | BV009016629 |
| classification_rvk | SI 320 SK 600 |
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| ctrlnum | (OCoLC)246643462 (DE-599)BVBBV009016629 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV009016629 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T13:02:16Z |
| institution | BVB |
| isbn | 0521448042 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005961979 |
| oclc_num | 246643462 |
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| physical | XII, 339 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Yukie, Akihiko Verfasser aut Shintani zeta functions Akihiko Yukie 1. publ. Cambridge Cambridge Univ. Press 1993 XII, 339 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 183 Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 183 (DE-604)BV000000130 183 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005961979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yukie, Akihiko Shintani zeta functions London Mathematical Society: London Mathematical Society lecture note series Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4190764-4 |
| title | Shintani zeta functions |
| title_auth | Shintani zeta functions |
| title_exact_search | Shintani zeta functions |
| title_full | Shintani zeta functions Akihiko Yukie |
| title_fullStr | Shintani zeta functions Akihiko Yukie |
| title_full_unstemmed | Shintani zeta functions Akihiko Yukie |
| title_short | Shintani zeta functions |
| title_sort | shintani zeta functions |
| topic | Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005961979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT yukieakihiko shintanizetafunctions |