An introduction to G-functions:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, New Jersey
Princeton University Press
1994
|
| Series: | Annals of mathematics studies
number 133 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxi, 323 Seiten graph. Darst. |
| ISBN: | 0691036756 0691036810 |
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MARC
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| 245 | 1 | 0 | |a An introduction to G-functions |c by Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan |
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Record in the Search Index
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| adam_text | CONTENTS
Preface xi
Introduction xiii
List of Symbols xix
CHAPTER I Valued Fields
1. Valuations 3
2. Complete Valued Fields 6
3. Normed Vector Spaces 8
4. Hensel s Lemma 10
5. Extensions of Valuations 17
6. Newton Polygons 24
7. The y-intercept Method 28
8. Ramification Theory 30
9. Totally Ramified Extensions 33
CHAPTER II Zeta Functions
1. Logarithms 38
2. Newton Polygons for Power Series 41
3. Newton Polygons for Laurent Series 46
4. The Binomial and Exponential Series 49
5. Dieudonne s Theorem 53
6. Analytic Representation of Additive Characters 56
7. Meromorphy of the Zeta Function of a Variety 61
8. Condition for Rationality 71
9. Rationality of the Zeta Function 74
Appendix to Chapter II 76
CHAPTER III Differential Equations
1. Differential Equations in Characteristic p 77
2. Nilpotent Differential Operators. Katz-Honda Theorem 81
3. Differential Systems 86
4. The Theorem of the Cyclic Vector 89
vii
viii CONTENTS
5. The Generic Disk. Radius of Convergence 92
6. Global Nilpotence. Katz s Theorem 98
7. Regular Singularities. Fuchs Theorem 100
8. Formal Fuchsian Theory 102
CHAPTER IV Effective Bounds. Ordinary Disks
1. p-adic Analytic Functions 114
2. Effective Bounds. The Dwork-Robba Theorem 119
3. Effective Bounds for Systems 126
4. Analytic Elements 128
5. Some Transfer Theorems 133
6. Logarithms 138
7. The Binomial Series 140
8. The Hypergeometric Function of Euler and Gauss 150
CHAPTER V Effective Bounds. Singular Disks
1. The Dwork-Frobenius Theorem 155
2. Effective Bounds for Solutions in a Singular Disk:
the Case of Nilpotent Monodromy.
The Christol-Dwork Theorem: Outline of the Proof 159
3. Proof of Step V 168
4. Proof of Step IV. The Shearing Transformation 169
5. Proof of Step III. Removing Apparent Singularities 170
6. The Operators j) and ip 173
7. Proof of Step I. Construction of Frobenius 176
8. Proof of Step II. Effective Form of the Cyclic Vector 180
9. Effective Bounds. The Case of Unipotent Monodromy 189
CHAPTER VI Transfer Theorems into Disks with One
Singularity
1. The Type of a Number 199
2. Transfer into Disks with One Singularity: a
First Estimate 203
3. The Theorem of Transfer of Radii of Convergence 212
CHAPTER VII Differential Equations of Arithmetic Type
1. The Height 222
2. The Theorem of Bombieri-Andre 226
3. Transfer Theorems for Differential Equations of
Arithmetic Type 234
CONTENTS ix
4. Size of Local Solution Bounded by its Global
Inverse Radius 243
5. Generic Global Inverse Radius Bounded by the Global
Inverse Radius of a Local Solution Matrix 254
CHAPTER VIII G-Series. The Theorem of Chudnovsky
1. Definition of G-Series.
Statement of Chudnovsky s Theorem 263
2. Preparatory Results 267
3. Siegel s Lemma 284
4. Conclusion of the Proof of Chudnovsky s Theorem 289
Appendix to Chapter VIII 300
APPENDIX I Convergence Polygon for Differential
Equations 301
APPENDIX II Archimedean Estimates 307
APPENDIX HI Cauchy s Theorem 310
Bibliography 317
Index 321
|
| any_adam_object | 1 |
| author | Dwork, Bernard M. 1923-1998 Gerotto, Giovanni Sullivan, Francis J. 1943- |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:40:30Z |
| institution | BVB |
| isbn | 0691036756 0691036810 |
| language | English |
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| physical | xxi, 323 Seiten graph. Darst. |
| publishDate | 1994 |
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| publisher | Princeton University Press |
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| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Dwork, Bernard M. 1923-1998 Verfasser (DE-588)117709654 aut An introduction to G-functions by Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan Princeton, New Jersey Princeton University Press 1994 © 1994 xxi, 323 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 133 G-Funktion (DE-588)4210136-0 gnd rswk-swf G-Funktion (DE-588)4210136-0 s DE-604 Gerotto, Giovanni Verfasser aut Sullivan, Francis J. 1943- Verfasser (DE-588)172758149 aut Elektronische Reproduktion 2016 9781400882540 Annals of mathematics studies number 133 (DE-604)BV000000991 133 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006460280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dwork, Bernard M. 1923-1998 Gerotto, Giovanni Sullivan, Francis J. 1943- An introduction to G-functions Annals of mathematics studies G-Funktion (DE-588)4210136-0 gnd |
| subject_GND | (DE-588)4210136-0 |
| title | An introduction to G-functions |
| title_auth | An introduction to G-functions |
| title_exact_search | An introduction to G-functions |
| title_full | An introduction to G-functions by Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan |
| title_fullStr | An introduction to G-functions by Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan |
| title_full_unstemmed | An introduction to G-functions by Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan |
| title_short | An introduction to G-functions |
| title_sort | an introduction to g functions |
| topic | G-Funktion (DE-588)4210136-0 gnd |
| topic_facet | G-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006460280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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