Shintani zeta functions:
The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated obj...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1993
|
| Series: | London Mathematical Society lecture note series
183 |
| Subjects: | |
| Online Access: | DE-12 DE-92 Volltext |
| Summary: | The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xii, 339 pages) |
| ISBN: | 9780511662331 |
| DOI: | 10.1017/CBO9780511662331 |
Staff View
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| 505 | 8 | |a pt. I. The general theory. Ch. 1. Preliminaries. Ch. 2. Eisenstein series on GL(n). Ch. 3. The general program -- pt. II. The Siegel-Shintani case. Ch. 4. The zeta function for the space of quadratic forms -- pt. III. Preliminaries for the quartic case. Ch. 5. The case G = GL(2) x GL(2), V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2]. Ch. 6. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k. Ch. 7. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2] -- pt. IV. The quartic case. Ch. 8. Invariant theory of pairs of ternary quadratic forms. Ch. 9. Preliminary estimates. Ch. 10. The non-constant terms associated with unstable strata. Ch. 11. Unstable distributions. Ch. 12. Contributions front unstable strata. Ch. 13. The main theorem | |
| 520 | |a The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory | ||
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Record in the Search Index
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| adam_text | |
| any_adam_object | |
| author | Yukie, Akihiko |
| author_facet | Yukie, Akihiko |
| author_role | aut |
| author_sort | Yukie, Akihiko |
| author_variant | a y ay |
| building | Verbundindex |
| bvnumber | BV043941680 |
| classification_rvk | SI 320 SK 600 |
| collection | ZDB-20-CBO |
| contents | pt. I. The general theory. Ch. 1. Preliminaries. Ch. 2. Eisenstein series on GL(n). Ch. 3. The general program -- pt. II. The Siegel-Shintani case. Ch. 4. The zeta function for the space of quadratic forms -- pt. III. Preliminaries for the quartic case. Ch. 5. The case G = GL(2) x GL(2), V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2]. Ch. 6. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k. Ch. 7. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2] -- pt. IV. The quartic case. Ch. 8. Invariant theory of pairs of ternary quadratic forms. Ch. 9. Preliminary estimates. Ch. 10. The non-constant terms associated with unstable strata. Ch. 11. Unstable distributions. Ch. 12. Contributions front unstable strata. Ch. 13. The main theorem |
| ctrlnum | (ZDB-20-CBO)CR9780511662331 (OCoLC)849894393 (DE-599)BVBBV043941680 |
| dewey-full | 515/.56 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511662331 |
| format | Electronic eBook |
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I. The general theory. Ch. 1. Preliminaries. Ch. 2. Eisenstein series on GL(n). Ch. 3. The general program -- pt. II. The Siegel-Shintani case. Ch. 4. The zeta function for the space of quadratic forms -- pt. III. Preliminaries for the quartic case. Ch. 5. The case G = GL(2) x GL(2), V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2]. Ch. 6. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k. Ch. 7. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2] -- pt. IV. The quartic case. Ch. 8. Invariant theory of pairs of ternary quadratic forms. Ch. 9. Preliminary estimates. Ch. 10. The non-constant terms associated with unstable strata. Ch. 11. Unstable distributions. Ch. 12. Contributions front unstable strata. Ch. 13. 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| id | DE-604.BV043941680 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T13:02:22Z |
| institution | BVB |
| isbn | 9780511662331 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350650 |
| oclc_num | 849894393 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xii, 339 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Yukie, Akihiko Verfasser aut Shintani zeta functions Akihiko Yukie Cambridge Cambridge University Press 1993 1 online resource (xii, 339 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 183 Title from publisher's bibliographic system (viewed on 05 Oct 2015) pt. I. The general theory. Ch. 1. Preliminaries. Ch. 2. Eisenstein series on GL(n). Ch. 3. The general program -- pt. II. The Siegel-Shintani case. Ch. 4. The zeta function for the space of quadratic forms -- pt. III. Preliminaries for the quartic case. Ch. 5. The case G = GL(2) x GL(2), V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2]. Ch. 6. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k. Ch. 7. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2] -- pt. IV. The quartic case. Ch. 8. Invariant theory of pairs of ternary quadratic forms. Ch. 9. Preliminary estimates. Ch. 10. The non-constant terms associated with unstable strata. Ch. 11. Unstable distributions. Ch. 12. Contributions front unstable strata. Ch. 13. The main theorem The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-44804-8 https://doi.org/10.1017/CBO9780511662331 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yukie, Akihiko Shintani zeta functions pt. I. The general theory. Ch. 1. Preliminaries. Ch. 2. Eisenstein series on GL(n). Ch. 3. The general program -- pt. II. The Siegel-Shintani case. Ch. 4. The zeta function for the space of quadratic forms -- pt. III. Preliminaries for the quartic case. Ch. 5. The case G = GL(2) x GL(2), V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2]. Ch. 6. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k. Ch. 7. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2] -- pt. IV. The quartic case. Ch. 8. Invariant theory of pairs of ternary quadratic forms. Ch. 9. Preliminary estimates. Ch. 10. The non-constant terms associated with unstable strata. Ch. 11. Unstable distributions. Ch. 12. Contributions front unstable strata. Ch. 13. The main theorem Functions, Zeta 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 | Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Functions, Zeta Zetafunktion |
| url | https://doi.org/10.1017/CBO9780511662331 |
| work_keys_str_mv | AT yukieakihiko shintanizetafunctions |