An introduction to the theory of local zeta functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2000
|
| Series: | American Mathematical Society: AMS/IP studies in advanced mathematics
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 232 S. |
| ISBN: | 082182015X |
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MARC
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| 245 | 1 | 0 | |a An introduction to the theory of local zeta functions |c Jun-ichi Igusa |
| 264 | 1 | |a Providence, RI |b AMS |c 2000 | |
| 300 | |a XII, 232 S. | ||
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| 490 | 1 | |a American Mathematical Society: AMS/IP studies in advanced mathematics |v 14 | |
| 650 | 4 | |a Fonctions zêta | |
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Record in the Search Index
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| adam_text |
Titel: An introduction to the theory of local zeta functions
Autor: Igusa, Jun-Ichi
Jahr: 2000
Contents
1 Preliminaries 1
1.1 Review of some basic theorems 1
1.2 Noetherian rings 5
1.3 Hilbert's theorems 8
2 Implicit function theorems and /('-analytic manifolds 15
2.1 Implicit function theorem 15
2.2 Implicit function theorem (non-archimedean case) 21
2.3 Weierstrass preparation theorem 24
2.4 K-analytic manifolds and differential forms 28
2.5 Critical sets and critical values 32
3 Hironaka's desingularization theorem 35
3.1 Monoidal transformations 35
3.2 Hironaka's desingularization theorem
(analytic form) 38
3.3 Desingularization of plane curves 40
4 Bernstein's theory 45
4.1 Bernstein's polynomial 6/(s) 45
4.2 Some properties of bj (s) 47
4.3 Reduction of the proof 49
4.4 A general theorem on D-modules 52
4.5 Completion of the proof 55
5 Archimedean local zeta functions 59
5.1 The group Q(KX) 59
5.2 Schwartz space S(Kn) 61
5.3 Local zeta function Z p(u ) 67
5.4 Complex power u;(/) via desingularization 73
5.5 An application 77
6 Prehomogeneous vector spaces 83
6.1 Sato's 6-function b(s) 83
6.2 The T-function (a digression) 87
6.3 b(s) = bf(s) and the rationality of the zeros 91
vii
viii
CONTENTS
7 Totally disconnected spaces and p-adic manifolds 97
7.1 Distributions in totally disconnected spaces 97
7.2 The case of homogeneous spaces 101
7.3 Structure of eigendistributions 106
7.4 Integration on p-adic manifolds 108
7.5 Serre's theorem on compact p-adic manifolds 113
7.6 Integration over the fibers 114
8 Local zeta functions (p-adic case) 117
8.1 Selfduality of K and some lemmas 117
8.2 p-adic zeta function Z j (cj) 120
8.3 Weil's functions Fq (i) and F£(i*) 125
8.4 Relation of F$,(i) and Z^(oj) 129
8.5 Poles of ijj(f) for a group invariant / 134
9 Some homogeneous polynomials 137
9.1 Quadratic forms and Witt's theorem 137
9.2 Quadratic forms over finite fields 141
9.3 Classical groups over finite fields 145
9.4 Composition and Jordan algebras 149
9.5 Norm forms and Freudenthal quartics 154
9.6 Gauss' identity and its corollaries 160
10 Computation of Z(s) 163
10.1 Z(oj) in some simple cases 163
10.2 A p-adic stationary phase formula 167
10.3 A key lemma 173
10.4 Z(s) for a Freudenthal quartic 178
10.5 Z(s) for the Gramian det(lxhx) 184
10.6 An integration formula 188
10.7 Z(s) for det(*a:/ia;) in product forms 193
11 Theorems of Denef and Meuser 199
11.1 Regular local rings 199
11.2 Geometric language 202
11.3 Hironaka's desingularization theorem
(algebraic form) 205
11.4 Weil's zeta functions over finite fields 210
11.5 Degree of Z(s) 214
11.6 The field Ke (a digression) 217
11.7 Functional equation of Z(s) 221
Bibliography 227
Index 231 |
| any_adam_object | 1 |
| author | Igusa, Jun-Ichi 1924-2013 |
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| author_facet | Igusa, Jun-Ichi 1924-2013 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013284192 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T13:02:18Z |
| institution | BVB |
| isbn | 082182015X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009056357 |
| oclc_num | 43296790 |
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| owner_facet | DE-355 DE-BY-UBR |
| physical | XII, 232 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | AMS |
| record_format | marc |
| series | American Mathematical Society: AMS/IP studies in advanced mathematics |
| series2 | American Mathematical Society: AMS/IP studies in advanced mathematics |
| spelling | Igusa, Jun-Ichi 1924-2013 Verfasser (DE-588)172162254 aut An introduction to the theory of local zeta functions Jun-ichi Igusa Providence, RI AMS 2000 XII, 232 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: AMS/IP studies in advanced mathematics 14 Fonctions zêta Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s DE-604 American Mathematical Society: AMS/IP studies in advanced mathematics 14 (DE-604)BV011103148 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009056357&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Igusa, Jun-Ichi 1924-2013 An introduction to the theory of local zeta functions American Mathematical Society: AMS/IP studies in advanced mathematics Fonctions zêta Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4190764-4 |
| title | An introduction to the theory of local zeta functions |
| title_auth | An introduction to the theory of local zeta functions |
| title_exact_search | An introduction to the theory of local zeta functions |
| title_full | An introduction to the theory of local zeta functions Jun-ichi Igusa |
| title_fullStr | An introduction to the theory of local zeta functions Jun-ichi Igusa |
| title_full_unstemmed | An introduction to the theory of local zeta functions Jun-ichi Igusa |
| title_short | An introduction to the theory of local zeta functions |
| title_sort | an introduction to the theory of local zeta functions |
| topic | Fonctions zêta Functions, Zeta Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Fonctions zêta Functions, Zeta Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009056357&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011103148 |
| work_keys_str_mv | AT igusajunichi anintroductiontothetheoryoflocalzetafunctions |