P-adic analysis compared with real:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2007]
|
| Series: | Student mathematical library
volume 37 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 152 Seiten Illustrationen |
| ISBN: | 9780821842201 |
Staff View
MARC
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| 100 | 1 | |a Katok, Svetlana |d 1947- |e Verfasser |0 (DE-588)11379679X |4 aut | |
| 245 | 1 | 0 | |a P-adic analysis compared with real |c Svetlana Katok |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2007] | |
| 264 | 4 | |c © 2007 | |
| 300 | |a xiii, 152 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v volume 37 | |
| 650 | 4 | |a Analyse p-adique | |
| 650 | 7 | |a Análise p-ádica |2 larpcal | |
| 650 | 7 | |a Teoria dos números |2 larpcal | |
| 650 | 4 | |a p-adic analysis | |
| 650 | 0 | 7 | |a p-adische Analysis |0 (DE-588)4252360-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804136562555879424 |
|---|---|
| adam_text | Contents
Foreword: MASS and
REU
at
Penn
State University
ix
Preface
xi
Chapter
1.
Arithmetic of the p-adic Numbers
1
§1.1.
From
Q
to R; the concept of completion
2
Exercises
1-8 5
§1.2.
Normed fields
6
Exercises
9-16 14
§1.3.
Construction of the completion of a normed field
15
Exercises
17-19 19
§1.4.
The field of p-adic numbers Qp
19
Exercises
20-25 26
§1.5.
Arithmetical operations in Qp
27
Exercises
26-31 30
§1.6.
The p-adic expansion of rational numbers
30
Exercises
32-34 33
§1.7.
Henseľs
Lemma and congruences
33
Exercises
35-44 38
§1.8.
Algebraic properties of p-
adic
integers
39
vi
Contents
§1.9.
Metrics and norms on the rational numbers.
Ostrowski s
Theorem
43
Exercises
45-46 47
§1.10.
A digression: what about Qg if
g
is not a prime?
47
Exercises
47-50 50
Chapter
2.
The Topology of Qp vs. the Topology of
R
53
§2.1.
Elementary topological properties
53
Exercises
51-53 60
§2.2.
Cantor sets
60
Exercises
54-65 68
§2.3.
Euclidean models of %v
69
Exercises
66-68 73
Chapter
3.
Elementary Analysis in Qp
75
§3.1.
Sequences and series
75
Exercises
69-73 80
§3.2.
p-adic power series
80
Exercises
74-78 86
§3.3.
Can a p-adic power series be analytically continued?
87
§3.4.
Some elementary functions
89
Exercises
79-81 92
§3.5.
Further properties of p-adic exponential and
logarithm
92
§3.6.
Zeros of p-adic power series
98
Exercises
82-83 102
Chapter
4.
p-adic Functions
103
§4.1.
Locally constant functions
103
Exercises
84-87 107
§4.2.
Continuous and uniformly continuous functions
108
Exercises
88-90 112
§4.3.
Points of discontinuity and the Baire Category
Theorem
112
Contents
vii
Exercises
91-96
115
§4.4.
Differentiability of p-adic functions
116
§4.5.
Isometries of Qp
121
Exercises
97-100
123
§4.6.
Interpolation
123
Exercises
101-103
134
Answers, Hints, and Solutions for Selected Exercises
135
Bibliography
149
Index
151
|
| adam_txt |
Contents
Foreword: MASS and
REU
at
Penn
State University
ix
Preface
xi
Chapter
1.
Arithmetic of the p-adic Numbers
1
§1.1.
From
Q
to R; the concept of completion
2
Exercises
1-8 5
§1.2.
Normed fields
6
Exercises
9-16 14
§1.3.
Construction of the completion of a normed field
15
Exercises
17-19 19
§1.4.
The field of p-adic numbers Qp
19
Exercises
20-25 26
§1.5.
Arithmetical operations in Qp
27
Exercises
26-31 30
§1.6.
The p-adic expansion of rational numbers
30
Exercises
32-34 33
§1.7.
Henseľs
Lemma and congruences
33
Exercises
35-44 38
§1.8.
Algebraic properties of p-
adic
integers
39
vi
Contents
§1.9.
Metrics and norms on the rational numbers.
Ostrowski 's
Theorem
43
Exercises
45-46 47
§1.10.
A digression: what about Qg if
g
is not a prime?
47
Exercises
47-50 50
Chapter
2.
The Topology of Qp vs. the Topology of
R
53
§2.1.
Elementary topological properties
53
Exercises
51-53 60
§2.2.
Cantor sets
60
Exercises
54-65 68
§2.3.
Euclidean models of %v
69
Exercises
66-68 73
Chapter
3.
Elementary Analysis in Qp
75
§3.1.
Sequences and series
75
Exercises
69-73 80
§3.2.
p-adic power series
80
Exercises
74-78 86
§3.3.
Can a p-adic power series be analytically continued?
87
§3.4.
Some elementary functions
89
Exercises
79-81 92
§3.5.
Further properties of p-adic exponential and
logarithm
92
§3.6.
Zeros of p-adic power series
98
Exercises
82-83 102
Chapter
4.
p-adic Functions
103
§4.1.
Locally constant functions
103
Exercises
84-87 107
§4.2.
Continuous and uniformly continuous functions
108
Exercises
88-90 112
§4.3.
Points of discontinuity and the Baire Category
Theorem
112
Contents
vii
Exercises
'91-96
115
§4.4.
Differentiability of p-adic functions
116
§4.5.
Isometries of Qp
121
Exercises
97-100
123
§4.6.
Interpolation
123
Exercises
101-103
134
Answers, Hints, and Solutions for Selected Exercises
135
Bibliography
149
Index
151 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:45:44Z |
| indexdate | 2024-07-09T20:58:22Z |
| institution | BVB |
| isbn | 9780821842201 |
| language | English |
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| publisher | American Mathematical Society |
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| series2 | Student mathematical library |
| spelling | Katok, Svetlana 1947- Verfasser (DE-588)11379679X aut P-adic analysis compared with real Svetlana Katok Providence, Rhode Island American Mathematical Society [2007] © 2007 xiii, 152 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 37 Analyse p-adique Análise p-ádica larpcal Teoria dos números larpcal p-adic analysis p-adische Analysis (DE-588)4252360-6 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2148-9 Student mathematical library volume 37 (DE-604)BV013184751 37 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015681497&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katok, Svetlana 1947- P-adic analysis compared with real Student mathematical library Analyse p-adique Análise p-ádica larpcal Teoria dos números larpcal p-adic analysis p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4252360-6 |
| title | P-adic analysis compared with real |
| title_auth | P-adic analysis compared with real |
| title_exact_search | P-adic analysis compared with real |
| title_exact_search_txtP | P-adic analysis compared with real |
| title_full | P-adic analysis compared with real Svetlana Katok |
| title_fullStr | P-adic analysis compared with real Svetlana Katok |
| title_full_unstemmed | P-adic analysis compared with real Svetlana Katok |
| title_short | P-adic analysis compared with real |
| title_sort | p adic analysis compared with real |
| topic | Analyse p-adique Análise p-ádica larpcal Teoria dos números larpcal p-adic analysis p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Analyse p-adique Análise p-ádica Teoria dos números p-adic analysis p-adische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015681497&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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