P-adic numbers: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Edition: | 2. ed., corr. 3. print. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 302 S. graph. Darst. |
| ISBN: | 3540629114 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Introduction 1
1 Aperitif 7
1.1 Hensel s Analogy 7
1.2 Solving Congruences Modulo pn 14
1.3 Other Examples 19
2 Foundations 23
2.1 Absolute Values on a Field 23
2.2 Basic Properties 29
2.3 Topology 32
2.4 Algebra 39
3 p adic Numbers 43
3.1 Absolute Values on Q 43
3.2 Completions 49
3.3 Exploring Qp 59
3.4 Hensel s Lemma 69
3.5 Local and Global 77
4 Elementary Analysis in Qp 87
4.1 Sequences and Series 88
4.2 Functions, Continuity, Derivatives 92
4.3 Power Series 95
4.4 Functions Defined by Power Series 102
4.5 Some Elementary Functions 111
4.6 Interpolation 126
5 Vector Spaces and Field Extensions 133
5.1 Normed Vector Spaces over Complete Valued Fields 134
5.2 Finite dimensional Normed Vector Spaces 139
5.3 Finite Field Extensions 143
5.4 Properties of Finite Extensions 158
5.5 Analysis 169
5.6 Example: Adjoining a p th Root of Unity 171
5.7 On to Cp 170
vi 0 Contents
6 Analysis in Cp 187
6.1 Almost Everything Extends 187
6.2 Deeper Results on Polynomials and Power Series 191
6.3 Entire Functions 208
6.4 Newton Polygons 212
6.5 Problems 231
A Hints and Comments on the Problems 235
B A Brief Glance at the Literature 291
B.I Texts 291
B.2 Software 292
B.3 Other Books 293
Bibliography 295
Index 299
|
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| discipline | Mathematik |
| edition | 2. ed., corr. 3. print. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:17:47Z |
| institution | BVB |
| isbn | 3540629114 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010495846 |
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| physical | VI, 302 S. graph. Darst. |
| publishDate | 2003 |
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| publishDateSort | 2003 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Gouvêa, Fernando Q. 1957- Verfasser (DE-588)111808863 aut P-adic numbers an introduction Fernando Q. Gouvêa 2. ed., corr. 3. print. Berlin [u.a.] Springer 2003 VI, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext P-adische getallen gtt p-adic numbers p-adische Zahl (DE-588)4044292-5 gnd rswk-swf p-adische Zahl (DE-588)4044292-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010495846&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gouvêa, Fernando Q. 1957- P-adic numbers an introduction P-adische getallen gtt p-adic numbers p-adische Zahl (DE-588)4044292-5 gnd |
| subject_GND | (DE-588)4044292-5 |
| title | P-adic numbers an introduction |
| title_auth | P-adic numbers an introduction |
| title_exact_search | P-adic numbers an introduction |
| title_full | P-adic numbers an introduction Fernando Q. Gouvêa |
| title_fullStr | P-adic numbers an introduction Fernando Q. Gouvêa |
| title_full_unstemmed | P-adic numbers an introduction Fernando Q. Gouvêa |
| title_short | P-adic numbers |
| title_sort | p adic numbers an introduction |
| title_sub | an introduction |
| topic | P-adische getallen gtt p-adic numbers p-adische Zahl (DE-588)4044292-5 gnd |
| topic_facet | P-adische getallen p-adic numbers p-adische Zahl |
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