Basic number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1995
|
| Ausgabe: | Reprint of the 1973 ed. |
| Schriftenreihe: | Classics in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Weitere Ausgabe: Grundlehren der mathematischen Wissenschaften ; 144 |
| Beschreibung: | XVIII, 312 S. |
| ISBN: | 3540586555 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV009979003 | ||
| 003 | DE-604 | ||
| 005 | 20111004 | ||
| 007 | t | ||
| 008 | 950102s1995 gw |||| 00||| ger d | ||
| 016 | 7 | |a 942768566 |2 DE-101 | |
| 020 | |a 3540586555 |c kart. : DM 59.00 |9 3-540-58655-5 | ||
| 035 | |a (OCoLC)258093672 | ||
| 035 | |a (DE-599)BVBBV009979003 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-92 |a DE-83 |a DE-11 |a DE-634 | ||
| 050 | 0 | |a QA241 | |
| 082 | 0 | |a 512.81 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a 17,1 |2 ssgn | ||
| 084 | |a 11Rxx |2 msc | ||
| 100 | 1 | |a Weil, André |d 1906-1998 |e Verfasser |0 (DE-588)118980963 |4 aut | |
| 245 | 1 | 0 | |a Basic number theory |c André Weil |
| 250 | |a Reprint of the 1973 ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XVIII, 312 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics in mathematics | |
| 500 | |a Weitere Ausgabe: Grundlehren der mathematischen Wissenschaften ; 144 | ||
| 650 | 4 | |a Class field theory | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Klassenkörpertheorie |0 (DE-588)4030951-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Klassenkörpertheorie |0 (DE-588)4030951-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 2 | |8 2\p |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006613647 | |
Datensatz im Suchindex
| _version_ | 1807502656537624576 |
|---|---|
| adam_text |
CONTENTS
CHRONOLOGICAL
TABLE
.
XII
PREREQUISITES
AND
NOTATIONS
.
XIII
TABLE
OF
NOTATIONS
.XVII
PART
I.
ELEMENTARY
THEORY
CHAPTER
I.
LOCALLY
COMPACT
FIELDS
.
1
§
1.
FINITE
FIELDS
.
1
§
2.
THE
MODULE
IN
A
LOCALLY
COMPACT
FIELD
.
3
§3.
CLASSIFICATION
OF
LOCALLY
COMPACT
FIELDS
.
8
§
4.
STRUCTURE
OF
P-FIELDS
.
12
CHAPTER
II.
LATTICES
AND
DUALITY
OVER
LOCAL
FIELDS
.
24
§
1.
NORMS
.
24
§2.
LATTICES
.
27
§3.
MULTIPLICATIVE
STRUCTURE
OF
LOCAL
FIELDS
.
31
§
4.
LATTICES
OVER
R
.
35
§
5.
DUALITY
OVER
LOCAL
FIELDS
.
38
CHAPTER
III.
PLACES
OF
A-FIELDS
.
43
§
1.
A-FIELDS
AND
THEIR
COMPLETIONS
.
43
§
2.
TENSOR-PRODUCTS
OF
COMMUTATIVE
FIELDS
.
48
§
3.
TRACES
AND
NORMS
.
52
§
4.
TENSOR-PRODUCTS
OF
A-FIELDS
AND
LOCAL
FIELDS
.
56
CHAPTER
IV.
ADELES
.
59
§
1.
ADELES
OF
A-FIELDS
.
59
§
2.
THE
MAIN
THEOREMS
.
64
§3.
IDELES
.
71
§
4.
IDELES
OF
A-FIELDS
.
75
X
CONTENTS
CHAPTER
V.
ALGEBRAIC
NUMBER-FIELDS
.
80
§
1.
ORDERS
IN
ALGEBRAS
OVER
Q
.
80
§2.
LATTICES
OVER
ALGEBRAIC
NUMBER-FIELDS
.
81
§
3.
IDEALS
.
85
§
4.
FUNDAMENTAL
SETS
.
89
CHAPTER
VI.
THE
THEOREM
OF
RIEMANN-ROCH
.
96
CHAPTER
VIL
ZETA-FUNCTIONS
OF
A-FIELDS
.
102
§
1.
CONVERGENCE
OF
EULER
PRODUCTS
.
102
§
2.
FOURIER
TRANSFORMS
AND
STANDARD
FUNCTIONS
.
104
§3.
QUASICHARACTERS
.
114
§
4.
QUASICHARACTERS
OF
A-FIELDS
.
118
§
5.
THE
FUNCTIONAL
EQUATION
.
120
§
6.
THE
DEDEKIND
ZETA-FUNCTION
.
127
§
7.
L-FUNCTIONS
.
130
§
8.
THE
COEFFICIENTS
OF
THE
L-SERIES
.
134
CHAPTER
VIII.
TRACES
AND
NORMS
.
139
§
1.
TRACES
AND
NORMS
IN
LOCAL
FIELDS
.
139
§
2.
CALCULATION
OF
THE
DIFFERENT
.
143
§
3.
RAMIFICATION
THEORY
.
147
§
4.
TRACES
AND
NORMS
IN
A-FIELDS
.
153
§
5.
SPLITTING
PLACES
IN
SEPARABLE
EXTENSIONS
.
158
§
6.
AN
APPLICATION
TO
INSEPARABLE
EXTENSIONS
.
159
PART
II.
CLASSFIELD
THEORY
CHAPTER
IX.
SIMPLE
ALGEBRAS
.
162
§1.
STRUCTURE
OF
SIMPLE
ALGEBRAS
.
162
§2.
THE
REPRESENTATIONS
OF
A
SIMPLE
ALGEBRA
.
168
§
3.
FACTOR-SETS
AND
THE
BRAUER
GROUP
.
170
§
4.
CYCLIC
FACTOR-SETS
.
180
§
5.
SPECIAL
CYCLIC
FACTOR-SETS
.
185
CHAPTER
X.
SIMPLE
ALGEBRAS
OVER
LOCAL
FIELDS
.
188
§
1.
ORDERS
AND
LATTICES
.
188
§
2.
TRACES
AND
NORMS
.
193
§
3.
COMPUTATION
OF
SOME
INTEGRALS
.
195
CONTENTS
XI
CHAPTER
XI.
SIMPLE
ALGEBRAS
OVER
A-FIELDS
.
202
§
1.
RAMIFICATION
.
202
§
2.
THE
ZETA-FUNCTION
OF
A
SIMPLE
ALGEBRA
.
203
§
3.
NORMS
IN
SIMPLE
ALGEBRAS
.
.
.
.
206
§
4.
SIMPLE
ALGEBRAS
OVER
ALGEBRAIC
NUMBER-FIELDS
.
210
CHAPTER
XII.
LOCAL
CLASSFIELD
THEORY
.
213
§
1.
THE
FORMALISM
OF
CLASSFIELD
THEORY
.
213
§
2.
THE
BRAUER
GROUP
OF
A
LOCAL
FIELD
.
220
§
3.
THE
CANONICAL
MORPHISM
.
226
§
4.
RAMIFICATION
OF
ABELIAN
EXTENSIONS
.
230
§
5.
THE
TRANSFER
.
240
CHAPTER
XIII.
GLOBAL
CLASSFIELD
THEORY
.
244
§
1.
THE
CANONICAL
PAIRING
.
244
§
2.
AN
ELEMENTARY
LEMMA
.
250
§
3.
HASSE
'
S
"
LAW
OF
RECIPROCITY
"
.
252
§
4.
CLASSFIELD
THEORY
FOR
Q
.
257
§
5.
THE
HILBERT
SYMBOL
.
260
§
6.
THE
BRAUER
GROUP
OF
AN
A-FIELD
.
264
§
7.
THE
HILBERT
P-SYMBOL
.
267
§
8.
THE
KERNEL
OF
THE
CANONICAL
MORPHISM
.
271
§
9.
THE
MAIN
THEOREMS
.
275
§
10.
LOCAL
BEHAVIOR
OF
ABELIAN
EXTENSIONS
.
277
§11.
"CLASSICAL
'
'
CLASSFIELD
THEORY
.
281
§
12.
"CORONIDIS
LOCO
"
.
288
NOTES
TO
THE
TEXT
.
292
APPENDIX
I.
THE
TRANSFER
THEOREM
.
295
APPENDIX
II.
IV-GROUPS
FOR
LOCAL
FIELDS
.
298
APPENDIX
III.
SHAFAREVITCH
'
S
THEOREM
.
301
APPENDIX
IV.
THE
HERBRAND
DISTRIBUTION
.
308
INDEX
OF
DEFINITIONS
. |
| any_adam_object | 1 |
| author | Weil, André 1906-1998 |
| author_GND | (DE-588)118980963 |
| author_facet | Weil, André 1906-1998 |
| author_role | aut |
| author_sort | Weil, André 1906-1998 |
| author_variant | a w aw |
| building | Verbundindex |
| bvnumber | BV009979003 |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241 |
| callnumber-search | QA241 |
| callnumber-sort | QA 3241 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)258093672 (DE-599)BVBBV009979003 |
| dewey-full | 512.81 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.81 |
| dewey-search | 512.81 |
| dewey-sort | 3512.81 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Reprint of the 1973 ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV009979003</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111004</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">950102s1995 gw |||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">942768566</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540586555</subfield><subfield code="c">kart. : DM 59.00</subfield><subfield code="9">3-540-58655-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)258093672</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV009979003</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-92</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA241</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.81</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11Rxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Weil, André</subfield><subfield code="d">1906-1998</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118980963</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Basic number theory</subfield><subfield code="c">André Weil</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Reprint of the 1973 ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 312 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Classics in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Weitere Ausgabe: Grundlehren der mathematischen Wissenschaften ; 144</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Class field theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Zahlentheorie</subfield><subfield code="0">(DE-588)4001170-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Klassenkörpertheorie</subfield><subfield code="0">(DE-588)4030951-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Zahlentheorie</subfield><subfield code="0">(DE-588)4001170-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Klassenkörpertheorie</subfield><subfield code="0">(DE-588)4030951-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006613647</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV009979003 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T00:40:58Z |
| institution | BVB |
| isbn | 3540586555 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006613647 |
| oclc_num | 258093672 |
| open_access_boolean | |
| owner | DE-92 DE-83 DE-11 DE-634 |
| owner_facet | DE-92 DE-83 DE-11 DE-634 |
| physical | XVIII, 312 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics |
| spelling | Weil, André 1906-1998 Verfasser (DE-588)118980963 aut Basic number theory André Weil Reprint of the 1973 ed. Berlin [u.a.] Springer 1995 XVIII, 312 S. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Weitere Ausgabe: Grundlehren der mathematischen Wissenschaften ; 144 Class field theory Number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Klassenkörpertheorie (DE-588)4030951-4 s Zahlentheorie (DE-588)4067277-3 s 2\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weil, André 1906-1998 Basic number theory Class field theory Number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd Zahlentheorie (DE-588)4067277-3 gnd Klassenkörpertheorie (DE-588)4030951-4 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4067277-3 (DE-588)4030951-4 (DE-588)4151278-9 |
| title | Basic number theory |
| title_auth | Basic number theory |
| title_exact_search | Basic number theory |
| title_full | Basic number theory André Weil |
| title_fullStr | Basic number theory André Weil |
| title_full_unstemmed | Basic number theory André Weil |
| title_short | Basic number theory |
| title_sort | basic number theory |
| topic | Class field theory Number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd Zahlentheorie (DE-588)4067277-3 gnd Klassenkörpertheorie (DE-588)4030951-4 gnd |
| topic_facet | Class field theory Number theory Algebraische Zahlentheorie Zahlentheorie Klassenkörpertheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT weilandre basicnumbertheory |