Number theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Edition: | Reprint of the 1980 ed. |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 638 S. Ill. |
| ISBN: | 354042749X 0387082751 |
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MARC
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| 100 | 1 | |a Hasse, Helmut |d 1898-1979 |e Verfasser |0 (DE-588)118708961 |4 aut | |
| 240 | 1 | 0 | |a Zahlentheorie |
| 245 | 1 | 0 | |a Number theory |c Helmut Hasse |
| 250 | |a Reprint of the 1980 ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XVII, 638 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics in mathematics | |
| 650 | 4 | |a Algebraische Zahlentheorie | |
| 650 | 4 | |a Number theory | |
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Record in the Search Index
| _version_ | 1804135934787059712 |
|---|---|
| adam_text | Table
of Contents
Part I. The Foundations of Arithmetic in the Rational Number Field
....... 1
Chapter
1.
Prime Decomposition
................... 2
Function Fields
...................... 7
Chapter
2.
Divisibility
........................ 8
Function Fields
...................... 22
Chapter
3.
Congruences
....................... 24
Function Fields
...................... 38
The Theory of Finite Fields
................ 40
Chapter
4.
The Structure of the Residue Class Ring mod
m
and of the Re¬
duced Residue Class Group mod
τη
............. 42
1.
General Facts Concerning Direct Products and Direct Sums
. 42
2.
Direct Decomposition of the Residue Class Ring mod
m
and of
the Reduced Residue Class Group mod
m
......... 46
3.
The Structure of the Additive Group of the Residue Class Ring
mod
m
........................ 55
4.
On the Structure of the Residue Class Ring mod p
.... 56
5.
The Structure of the Reduced Residue Class Group mod
ρμ
57
Function Fields
..................... 63
Chapter
5.
Quadratic Residues
..................... 64
1.
Theory of the Characters of a Finite Abelian Group
..... 64
2.
Residue Class Characters and Numerical Characters mod
m
. 69
3.
The Basic Facts Concerning Quadratic Residues
...... 73
4.
The Quadratic Reciprocity Law for the Legendre Symbol
. . 77
5.
The Quadratic Reciprocity Law for the Jacobi Symbol
... 83
6.
The Quadratic Reciprocity Law as Product Formula for the
Hubert Symbol
.................... 92
7.
Special Cases of Dirichlet s Theorem on Prime Numbers in
Reduced Residue Classes
................ 96
Function Field
..................... 100
Part
Π.
The Theory
oí
Valued Fields
..................... 105
Chapter
6.
The Fundamental Concepts Regarding Valuations
....... 105
1.
The Definition of a Valuation; Equivalent Valuations
.... 105
2.
Approximation Independence and Multiplicative Independence
of Valuations
..................... 109
3.
Valuations of the Prime Field
.............. 113
4.
Value Groups and Residue Class Fields
.......... 122
Function Fields
..................... 126
XIV
Table of Contents
Chapter
7.
Arithmetic in a Discrete Valued Field
............129
Divisors from an Ideal-Theoretic Standpoint
.........133
Chapter
8.
The Completion of a Valued Field
..............136
Chapter
9.
The Completion of a Discrete Valued Field. The jp-adic Number
Fields
..........................144
Function Fields
......................149
Chapter
10.
The Isomorphism Types of Complete Discrete Valued Fields
with Perfect Residue Class Field
.............. 161
1.
The
Multiplicative
Residue System in the Case of Prime Cha¬
racteristic
....................... 152
2.
The Equal-Characteristic Case with Prime Characteristic
. . 154
3.
The Multiplicative Residue System in the #-adic Number
Field
........................ . 155
4.
Witt s Vector Calculus
................. 156
5.
Construction of the General jj-adic Field
......... 161
6.
The Unequal-Characteristic Case
............. 165
7.
Isomorphic Residue Systems in the Case of Characteristic
0 . 169
8.
The Isomorphic Residue Systems for a Rational Function
Field
......................... 174
9.
The Equal-Characteristic Case with Characteristic
0 .... 174
Chapter
11.
Prolongation of a Discrete Valuation to a Purely Transcendental
Extension
........................176
Chapter
12.
Prolongation of the Valuation of a Complete Field to a Finite-
Algebraic Extension
................... 182
1.
The Proof of Existence
................. 184
2.
The Proof of Completeness
................ 188
3.
The Proof of Uniqueness
................ 190
Chapter
13.
The Isomorphism Types of Complete Archimedean Valued Fields
191
Chapter
14.
The Structure of a Finite-Algebraic Extension of a Complete
Discrete Valued Field
................... 194
1.
Embedding of the Arithmetic
.............. 195
2.
The Totally Ramified Case
............... 201
3.
The Unramified Case with Perfect Residue Class Field
... 203
4.
The General Case with Perfect Residue Class Field
..... 208
5.
The General Case with Finite Residue Class Field
..... 210
Chapter
15.
The Structure of the Multiplicative Group of a Complete Discrete
Valued Field with Perfect Residue Class Field of Prime Charac¬
teristic
...................... .... 213
1.
Reduction to the One-Unit Group and its Fundamental Chain
of Subgroups
...................... 213
2.
The One-Unit Group as an Abelian Operator Group
.... 215
3.
The Field of nth Roots of Unity over a
јз
-adic
Number Field
219
4.
The Structure of the One-Unit Group in the Equal-Charac¬
teristic Case with Finite Residue Class Field
........ 225
5.
The Structure of the One-Unit Group in the p-adic Case
. . 228
6.
Construction of a System of Fundamental One-Unite in the
p-adic Case
...................... 233
7.
The One-Unit Group for Special p-adie Number Fields
. . . 246
8.
Comparison of the Basis Representation of the Multiplicative
Group in the p-adic Case and the Archimedean Case
.... 247
Chapter
16.
The Tamely Ramified Extension Types of a Complete Discrete
Valued Field with Finite Residue Class Field of Characteristic
ρ
248
Table
of
Contents
XV
ChapteF
17.
The Exponential Function, the Logarithm, and Powers in a Com¬
plete
Non-
Archimedean Valued Field of Characteristic
0 ... 255
1.
Integral Power Series in One Indeterminate over an Arbitrary
Field
.........................255
2.
Integral Power Series in One Variable in a Complete
Non-
Archi¬
medean Valued Field
.................. 256
3.
Convergence
......................262
4.
Functional Equations and Mutual Relations
........266
5.
The Discrete Case
...................274
6.
The
E
qual
-Characteristic Case with Characteristic
0 .... 276
Chapter
18.
Prolongation of the Valuation of a Non-Complete Field to a
Finite-Algebraic Extension
.................276
1.
Representations of a Separable Finite-Algebraic Extension
over an Arbitrary Extension of the Ground Field
.....279
2.
The Ring Extension of a Separable Finite-Algebraic Extension
by an Arbitrary Ground Field Extension, or the Tensor Product
of the Two Field Extensions
................ 283
3.
The Characteristic Polynomial
.............. 294
4.
Supplements for Inseparable Extensions
.......... 297
5.
Prolongation of a Valuation
....... ....... 298
6.
The Discrete Case
................... 302
7.
The Archimedean Case
................. 305
Part III. The Foundations of Arithmetic in Algebraic Number Fields
.......309
Chapter
19.
Relations Between the Complete System of Valuations and the
Arithmetic of the Rational Number Field
.......... 310
1.
Finiteness Properties
.................. 310
2.
Characterizations in Divisibility Theory
.......... 310
3.
The Product Formula for Valuations
........... 311
4.
The Sum Formula for the Principal Parts
......... 312
Function Fields
..................... 315
The Automorphisms of
α
Rational Function Field
..... 322
Chapter
20.
Prolongation of the Complete System of Valuations to a Finite-
Algebraic Extension
................... 324
Function Fields
...................... 328
Concluding Remarks
................... 334
Chapter
21.
The Prime Spots of an Algebraic Number Field and their Com¬
pletions
.........................335
Function Fields
......................337
Chapter
22.
Decomposition into Prime Divisors, Integrality, and Divisibility
338
1.
The Canonical Homomorphism of the Multiplicative Group
into the Divisor Group
................. 338
2.
Embedding of Divisibility Theory under a Finite-Algebraic
Extension
....................... 344
3.
Algebraic Characterization of Integral Algebraic Numbers
. . 351
4.
Quotient Representation
................ 353
Function Fields
.................... 354
Constant Fields, Constant Extensions
........... 362
Chapter
23.
Congruences
.......................367
1.
Ordinary Congruence
..................368
2.
Multiplicative Congruence
................370
Function Fields
....................372
XVI Table of Contents
Chapter
24.
The Multiples of a Divisor
................. 372
1·
Field Bases
...................... 373
2.
The Ideal Property, Ideal Bases
............. 375
3.
Congruences for Integral Elements
............ 378
4-
Divisors from the Ideal-Theoretic Standpoint
....... 383
5.
Further Remarks Concerning Divisors and Ideals
..... 389
Function Fields
....................393
Constant Fields for p. Characterization of Prime Divisors by
Homomorphisms. Decomposition Law under an Algebraic
Constant Extension
...................402
The Rank of the Module of Multiples of a Divisor
......419
Chapter
25.
Différents
and Discriminants
................ 429
1.
Composition Formula for the Trace and Norm. The Divisor
Trace
......................... 430
2.
Definition of the Different and Discriminant
........ 433
3.
Theorems on
Différents
and Discriminants in the Small
. . . 435
*·
The Relationship Between
Différents
and Discriminants in
the Small and in the Large
............... 442
5.
Theorems on
Differente
and Discriminants in the Large
. . 443
6.
Common Inessential Discriminant Divisors
........ 452
7.
Examples
....................... 457
Function Fields
.................... 462
The Number of First-Degree Prime Divisors in the
Саве
of a
Finite Constant Field
.................. 464
Differentials
...................... 467
The Riemann-Pvoch Theorem and its Consequences
..... 473
Disclosed Algebraio Function Fields
............ 484
Chapter
26.
Quadratic Number Fields
.................494
1·
Generation in the Large and in the Small
......... 494
2.
The Decomposition Law
.................496
3.
Discriminants, Integral Bases
..............498
4.
Quadratic Besidue Characters of the Discriminant of an
Arbitrary Algebraic Number Field
............501
5.
The Quadratic Number Fields as Class Fields
.......504
6.
The Hubert Symbol as Norm Symbol
...........505
7.
The Norm Theorem
..................510
8.
A Necessary Condition for Principal Divisors. Genera
.... 512
Chapter
27.
Cyclotomic Fields
.....................520
1.
Generation
......................520
2.
The Decomposition Law
................522
3.
Discriminants, Integral Bases
..............523
4.
The Quadratic Number Fields as Subfields of Cyclotomic
Fields
.........................528
Chapter
28.
Units
..........................
536
1·
Preliminaries
...................... 536
2.
Proofs
........................ 540
3.
Extension
....................... 549
4.
Examples and Applications
............... 550
Chapter
29.
The Class Number
.................... 562
1·
Finiteness of the Class Number
............. 562
2· Consequences
..................... 563
3.
Examples and Applications
............... 565
Function Fields
.................... 594
Table of Contents
XVII
Chapter
30.
Approximation Theorems and Estimates of the Discriminant
. . 696
1.
The Most General Requirements on Approximating Zero
. . 697
2.
Minkowski s Lattice-Point Theorem
........... 600
3.
Application to Convex Bodies within the Norm-one Hyper-
surface
........................ 603
4.
Consequencee of the Discriminant Estimate
........ 616
Function Fields
.....................626
Index of Names
..............................628
Subject Index
...............................629
|
| adam_txt |
Table
of Contents
Part I. The Foundations of Arithmetic in the Rational Number Field
. 1
Chapter
1.
Prime Decomposition
. 2
Function Fields
. 7
Chapter
2.
Divisibility
. 8
Function Fields
. 22
Chapter
3.
Congruences
. 24
Function Fields
. 38
The Theory of Finite Fields
. 40
Chapter
4.
The Structure of the Residue Class Ring mod
m
and of the Re¬
duced Residue Class Group mod
τη
. 42
1.
General Facts Concerning Direct Products and Direct Sums
. 42
2.
Direct Decomposition of the Residue Class Ring mod
m
and of
the Reduced Residue Class Group mod
m
. 46
3.
The Structure of the Additive Group of the Residue Class Ring
mod
m
. 55
4.
On the Structure of the Residue Class Ring mod p"
. 56
5.
The Structure of the Reduced Residue Class Group mod
ρμ
57
Function Fields
. 63
Chapter
5.
Quadratic Residues
. 64
1.
Theory of the Characters of a Finite Abelian Group
. 64
2.
Residue Class Characters and Numerical Characters mod
m
. 69
3.
The Basic Facts Concerning Quadratic Residues
. 73
4.
The Quadratic Reciprocity Law for the Legendre Symbol
. . 77
5.
The Quadratic Reciprocity Law for the Jacobi Symbol
. 83
6.
The Quadratic Reciprocity Law as Product Formula for the
Hubert Symbol
. 92
7.
Special Cases of Dirichlet's Theorem on Prime Numbers in
Reduced Residue Classes
. 96
Function Field
. 100
Part
Π.
The Theory
oí
Valued Fields
. 105
Chapter
6.
The Fundamental Concepts Regarding Valuations
. 105
1.
The Definition of a Valuation; Equivalent Valuations
. 105
2.
Approximation Independence and Multiplicative Independence
of Valuations
. 109
3.
Valuations of the Prime Field
. 113
4.
Value Groups and Residue Class Fields
. 122
Function Fields
. 126
XIV
Table of Contents
Chapter
7.
Arithmetic in a Discrete Valued Field
.129
Divisors from an Ideal-Theoretic Standpoint
.133
Chapter
8.
The Completion of a Valued Field
.136
Chapter
9.
The Completion of a Discrete Valued Field. The jp-adic Number
Fields
.144
Function Fields
.149
Chapter
10.
The Isomorphism Types of Complete Discrete Valued Fields
with Perfect Residue Class Field
. 161
1.
The
Multiplicative
Residue System in the Case of Prime Cha¬
racteristic
. 152
2.
The Equal-Characteristic Case with Prime Characteristic
. . 154
3.
The Multiplicative Residue System in the #-adic Number
Field
. . 155
4.
Witt's Vector Calculus
. 156
5.
Construction of the General jj-adic Field
. 161
6.
The Unequal-Characteristic Case
. 165
7.
Isomorphic Residue Systems in the Case of Characteristic
0 . 169
8.
The Isomorphic Residue Systems for a Rational Function
Field
. 174
9.
The Equal-Characteristic Case with Characteristic
0 . 174
Chapter
11.
Prolongation of a Discrete Valuation to a Purely Transcendental
Extension
.176
Chapter
12.
Prolongation of the Valuation of a Complete Field to a Finite-
Algebraic Extension
. 182
1.
The Proof of Existence
. 184
2.
The Proof of Completeness
. 188
3.
The Proof of Uniqueness
. 190
Chapter
13.
The Isomorphism Types of Complete Archimedean Valued Fields
191
Chapter
14.
The Structure of a Finite-Algebraic Extension of a Complete
Discrete Valued Field
. 194
1.
Embedding of the Arithmetic
. 195
2.
The Totally Ramified Case
. 201
3.
The Unramified Case with Perfect Residue Class Field
. 203
4.
The General Case with Perfect Residue Class Field
. 208
5.
The General Case with Finite Residue Class Field
. 210
Chapter
15.
The Structure of the Multiplicative Group of a Complete Discrete
Valued Field with Perfect Residue Class Field of Prime Charac¬
teristic
. . 213
1.
Reduction to the One-Unit Group and its Fundamental Chain
of Subgroups
. 213
2.
The One-Unit Group as an Abelian Operator Group
. 215
3.
The Field of nth Roots of Unity over a
јз
-adic
Number Field
219
4.
The Structure of the One-Unit Group in the Equal-Charac¬
teristic Case with Finite Residue Class Field
. 225
5.
The Structure of the One-Unit Group in the p-adic Case
. . 228
6.
Construction of a System of Fundamental One-Unite in the
p-adic Case
. 233
7.
The One-Unit Group for Special p-adie Number Fields
. . . 246
8.
Comparison of the Basis Representation of the Multiplicative
Group in the p-adic Case and the Archimedean Case
. 247
Chapter
16.
The Tamely Ramified Extension Types of a Complete Discrete
Valued Field with Finite Residue Class Field of Characteristic
ρ
248
Table
of
Contents
XV
ChapteF
17.
The Exponential Function, the Logarithm, and Powers in a Com¬
plete
Non-
Archimedean Valued Field of Characteristic
0 . 255
1.
Integral Power Series in One Indeterminate over an Arbitrary
Field
.255
2.
Integral Power Series in One Variable in a Complete
Non-
Archi¬
medean Valued Field
. 256
3.
Convergence
.262
4.
Functional Equations and Mutual Relations
.266
5.
The Discrete Case
.274
6.
The
E
qual
-Characteristic Case with Characteristic
0 . 276
Chapter
18.
Prolongation of the Valuation of a Non-Complete Field to a
Finite-Algebraic Extension
.276
1.
Representations of a Separable Finite-Algebraic Extension
over an Arbitrary Extension of the Ground Field
.279
2.
The Ring Extension of a Separable Finite-Algebraic Extension
by an Arbitrary Ground Field Extension, or the Tensor Product
of the Two Field Extensions
. 283
3.
The Characteristic Polynomial
. 294
4.
Supplements for Inseparable Extensions
. 297
5.
Prolongation of a Valuation
. . 298
6.
The Discrete Case
. 302
7.
The Archimedean Case
. 305
Part III. The Foundations of Arithmetic in Algebraic Number Fields
.309
Chapter
19.
Relations Between the Complete System of Valuations and the
Arithmetic of the Rational Number Field
. 310
1.
Finiteness Properties
. 310
2.
Characterizations in Divisibility Theory
. 310
3.
The Product Formula for Valuations
. 311
4.
The Sum Formula for the Principal Parts
. 312
Function Fields
. 315
The Automorphisms of
α
Rational Function Field
. 322
Chapter
20.
Prolongation of the Complete System of Valuations to a Finite-
Algebraic Extension
. 324
Function Fields
. 328
Concluding Remarks
. 334
Chapter
21.
The Prime Spots of an Algebraic Number Field and their Com¬
pletions
.335
Function Fields
.337
Chapter
22.
Decomposition into Prime Divisors, Integrality, and Divisibility
338
1.
The Canonical Homomorphism of the Multiplicative Group
into the Divisor Group
. 338
2.
Embedding of Divisibility Theory under a Finite-Algebraic
Extension
. 344
3.
Algebraic Characterization of Integral Algebraic Numbers
. . 351
4.
Quotient Representation
. 353
Function Fields
. 354
Constant Fields, Constant Extensions
. 362
Chapter
23.
Congruences
.367
1.
Ordinary Congruence
.368
2.
Multiplicative Congruence
.370
Function Fields
.372
XVI Table of Contents
Chapter
24.
The Multiples of a Divisor
. 372
1·
Field Bases
. 373
2.
The Ideal Property, Ideal Bases
. 375
3.
Congruences for Integral Elements
. 378
4-
Divisors from the Ideal-Theoretic Standpoint
. 383
5.
Further Remarks Concerning Divisors and Ideals
. 389
Function Fields
.393
Constant Fields for p. Characterization of Prime Divisors by
Homomorphisms. Decomposition Law under an Algebraic
Constant Extension
.402
The Rank of the Module of Multiples of a Divisor
.419
Chapter
25.
Différents
and Discriminants
. 429
1.
Composition Formula for the Trace and Norm. The Divisor
Trace
. 430
2.
Definition of the Different and Discriminant
. 433
3.
Theorems on
Différents
and Discriminants in the Small
. . . 435
*·
The Relationship Between
Différents
and Discriminants in
the Small and in the Large
. 442
5.
Theorems on
Differente
and Discriminants in the Large
. . 443
6.
Common Inessential Discriminant Divisors
. 452
7.
Examples
. 457
Function Fields
. 462
The Number of First-Degree Prime Divisors in the
Саве
of a
Finite Constant Field
. 464
Differentials
. 467
The Riemann-Pvoch Theorem and its Consequences
. 473
Disclosed Algebraio Function Fields
. 484
Chapter
26.
Quadratic Number Fields
.494
1·
Generation in the Large and in the Small
. 494
2.
The Decomposition Law
.496
3.
Discriminants, Integral Bases
.498
4.
Quadratic Besidue Characters of the Discriminant of an
Arbitrary Algebraic Number Field
.501
5.
The Quadratic Number Fields as Class Fields
.504
6.
The Hubert Symbol as Norm Symbol
.505
7.
The Norm Theorem
.510
8.
A Necessary Condition for Principal Divisors. Genera
. 512
Chapter
27.
Cyclotomic Fields
.520
1.
Generation
.520
2.
The Decomposition Law
.522
3.
Discriminants, Integral Bases
.523
4.
The Quadratic Number Fields as Subfields of Cyclotomic
Fields
.528
Chapter
28.
Units
.
536
1·
Preliminaries
. 536
2.
Proofs
. 540
3.
Extension
. 549
4.
Examples and Applications
. 550
Chapter
29.
The Class Number
. 562
1·
Finiteness of the Class Number
. 562
2· Consequences
. 563
3.
Examples and Applications
. 565
Function Fields
. 594
Table of Contents
XVII
Chapter
30.
Approximation Theorems and Estimates of the Discriminant
. . 696
1.
The Most General Requirements on Approximating Zero
. . 697
2.
Minkowski's Lattice-Point Theorem
. 600
3.
Application to Convex Bodies within the Norm-one Hyper-
surface
. 603
4.
Consequencee of the Discriminant Estimate
. 616
Function Fields
.626
Index of Names
.628
Subject Index
.629 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hasse, Helmut 1898-1979 |
| author_GND | (DE-588)118708961 |
| author_facet | Hasse, Helmut 1898-1979 |
| author_role | aut |
| author_sort | Hasse, Helmut 1898-1979 |
| author_variant | h h hh |
| building | Verbundindex |
| bvnumber | BV021965558 |
| 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)248459133 (DE-599)BVBBV021965558 |
| dewey-full | 512.7 512/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 512/.7 |
| dewey-search | 512.7 512/.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Reprint of the 1980 ed. |
| format | Book |
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| id | DE-604.BV021965558 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:08:53Z |
| indexdate | 2024-07-09T20:48:24Z |
| institution | BVB |
| isbn | 354042749X 0387082751 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015180708 |
| oclc_num | 248459133 |
| open_access_boolean | |
| owner | DE-706 DE-384 DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-706 DE-384 DE-11 DE-19 DE-BY-UBM |
| physical | XVII, 638 S. Ill. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics |
| spelling | Hasse, Helmut 1898-1979 Verfasser (DE-588)118708961 aut Zahlentheorie Number theory Helmut Hasse Reprint of the 1980 ed. Berlin [u.a.] Springer 2002 XVII, 638 S. Ill. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Algebraische Zahlentheorie Number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015180708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hasse, Helmut 1898-1979 Number theory Algebraische Zahlentheorie Number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4067277-3 |
| title | Number theory |
| title_alt | Zahlentheorie |
| title_auth | Number theory |
| title_exact_search | Number theory |
| title_exact_search_txtP | Number theory |
| title_full | Number theory Helmut Hasse |
| title_fullStr | Number theory Helmut Hasse |
| title_full_unstemmed | Number theory Helmut Hasse |
| title_short | Number theory |
| title_sort | number theory |
| topic | Algebraische Zahlentheorie Number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Algebraische Zahlentheorie Number theory Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015180708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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