Distribution theory of algebraic numbers:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Gruyter
2008
|
| Series: | De Gruyter expositions in mathematics
45 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 527 S. |
| ISBN: | 9783110205367 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
CONTENTS PREFACE V 1 FIELD EXTENSIONS 1 1.1 GROUPS 1 1.1.1 ABELIAN
GROUPS 1 1.1.2 GALOIS COHOMOLOGY 7 1.2 RINGS AND IDEALS 9 1.2.1 IDEALS 9
1.2.2 COMPLETION OF TOPOLOGICAL GROUPS 16 1.2.3 FRACTIONAL IDEALS 18
1.2.4 RELATIVE DIFFERENTIALS 19 1.3 INTEGRAL ELEMENTS AND VALUATIONS 21
1.3.1 INTEGRAL ELEMENTS 21 1.3.2 VALUATION RINGS 23 1.3.3 DISCRETE
VALUATION RINGS 27 1.4 POLYNOMIALS 32 1.5 ALGEBRAIC EXTENSION FIELDS 36
1.6 SEPARABLE EXTENSION FIELDS 41 1.6.1 SEPARABLE ALGEBRAIC EXTENSIONS
41 1.6.2 RAMIFICATION INDICES 45 1.7 NORM AND TRACE 47 1.8 DISCRIMINANT
OF FIELD EXTENSIONS 52 1.9 ABSOLUTE VALUES ON FIELDS 55 1.9.1 ABSOLUTE
VALUES 55 1.9.2 EXTENSIONS OF ABSOLUTE VALUES 58 1.9.3 EXTENSIONS OF
VALUATIONS 60 1.10 DIVISOR GROUPS 71 1.10.1 VALUATION PROPERTIES OF
DEDEKIND DOMAINS 71 1.10.2 LOCAL DEGREES IN FIELD EXTENSIONS 78 1.11
DIFFERENT 84 2 ALGEBRAK NUMBERS 91 2.1 INTEGRAL IDEALS 91 2.1.1
FACTORIZATIONOF IDEALS 91 2.1.2 THE NORMOF AN IDEAL 99 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/990069141 DIGITALISIERT DURCH 3.7.1
SCHEINES 212 VIII CONTENTS 2.2 ABSOLUTE VALUES ON NUMBER FIELDS 101
2.2.1 ARCHIMEDEAN ABSOLUTE VALUES 102 2.2.2 PRODUCT FORMULA 103 2.2.3
GALOIS EXTENSIONS OF NUMBER FIELDS 108 2.3 DISCRIMINANT OF NUMBER FIELDS
109 2.4 MINKOWSKI'S GEOMETRY OF NUMBERS 112 2.4.1 MINKOWSKI'S
FIRSTTHEOREM 112 2.4.2 MINKOWSKI'S BOUND 116 2.4.3 DIRICHLET'S UNIT
THEOREM 120 2.4.4 MINKOWSKI'S SECOND THEOREM 123 2.5 DIFFERENT OF NUMBER
FIELDS 124 3 ALGEBRAIC GEOMETRY 130 3.1 HERMITIAN GEOMETRY 130 3.1.1
EXTERIOR PRODUCT 130 3.1.2 NORMS OF VECTOR SPACES 132 3.1.3 SCHWARZ
INEQUALITIES 136 3.1.4 GENERAL POSITION 140 3.1.5 HYPERSURFACES 144 3.2
VARIETIES 150 3.2.1 AFFINE VARIETIES 150 3.2.2 PROJECTIVE VARIETIES 154
3.2.3 LOCAL RINGS OF VARIETIES 156 3.2.4 DIMENSIONS 160 3.2.5
DIFFERENTIAL FORMS 162 3.2.6 ABELIAN VARIETIES 165 3.3 DIVISORS 167 3.4
LINEAR SYSTEMS 173 3.5 ALGEBRAIC CURVES 177 3.5.1 BEZOUT'S THEOREM 177
3.5.2 RIEMANN-ROCH THEOREM 181 3.5.3 RATIONAL CURVES 184 3.5.4 ELLIPTIC
CURVES 186 3.5.5 HYPERELLIPTIC CURVES 194 3.5.6 JACOBIAN OF CURVES 196
3.6 SHEAVES AND VECTOR BUNDLES 197 3.6.1 SHEAVES 197 3.6.2 VECTOR
BUNDLES 202 3.6.3 LINE BUNDLES 206 3.6.4 INTERSECTION MULTIPLICITY 209
3.7 SCHEINES 212 CONTENTS IX 3.7.2 BASIC PROPERTIES OF SCHEMES 219 3.7.3
SHEAVES OF MODULES 224 3.7.4 DIFFERENTIALS OVER SCHEMES 224 3.7.5
RAMIFICATION DIVISORS 226 3.8 KOBAYASHI HYPERBOLICITY 229 3.8.1
HYPERBOLICITY 229 3.8.2 MEASURE HYPERBOLICITY 232 3.8.3 OPEN PROBLEMS
237 4 HEIGHT FUNCTIONS 239 4.1 HEIGHTS ON PROJECTIVE SPACES 239 4.1.1
BASIC PROPERTIES 239 4.1.2 HEIGHTS ON NUMBER FIELDS 242 4.1.3 FUNCTIONAL
PROPERTIES OF HEIGHTS 247 4.2 HEIGHTS OF POLYNOMIALS 250 4.2.1
COEFFICIENTS FOR POLYNOMIALS 250 4.2.2 GELFAND'S INEQUALITY 255 4.2.3
FINITENESS THEOREMS 259 4.3 HEIGHTS ON VARIETIES 264 4.4 HEIGHTS AND
WEIL FUNCTIONS 274 4.4.1 WEIL FUNCTIONS 274 4.4.2 HEIGHTS EXPAND WEIL
FUNCTIONS 278 4.4.3 PROXIMITY FUNCTIONS 280 4.5 ARAKELOV THEORY 283
4.5.1 FUNCTION FIELDS 283 4.5.2 NUMBER FIELDS 286 4.6 CANONICAL HEIGHTS
ON ABELIAN VARIETIES 294 4.6.1 PERIODIC POINTS 294 4.6.2 CANONICAL
HEIGHTS 297 4.6.3 TATE-SHAFAREVICH GROUPS 299 4.6.4 MORDELL-WEIL THEOREM
301 5 THE ABC-CONJECTURE 304 5.1 THE A&C-THEOREM FOR FUNCTION FIELDS 304
5.2 THE A&C-CONJECTURE FOR INTEGERS 306 5.3 EQUIVALENT A&C-CONJECTURE
308 5.4 GENERALIZED A&C-CONJEETURE 312 5.5 GENERALIZED HALFS CONJECTURE
315 5.6 THE A&C-CONJECTURE FOR NUMBER FIELDS CONTENTS ROTH'S THEOREM 328
6.1 STATEMENT OF THE THEOREM 328 6.2 SIEGEL'SLEMMA 331 6.3 INDICES OF
POLYNOMIALS 335 6.4 ROTH'S LEMMA 340 6.5 PROOF OF ROTH'S THEOREM 346 6.6
FORMULATION OF ROTH'S THEOREM 351 6.6.1 A GENERALIZATION 351 6.6.2
APPROACH INFINITY 352 6.6.3 RAMIFICATION TERM 354 6.6.4 ROTH'S THEOREM
AND A&C-CONJECTURE 358 SUBSPACE THEOREMS 360 7.1 P-ADIC MINKOWSKI'S
SECOND THEOREM 360 7.2 ADELIC MINKOWSKI'S SECOND THEOREM 366 7.2.1
HAARMEASURES 366 7.2.2 ADELE RINGS 368 7.2.3 MINKOWSKI'S SECOND THEOREM
371 7.3 SUCCESSIVE MINIMA OF A LENGTH FUNCTION 379 7.4 VOJTA'S ESTIMATE
386 7.5 SCHMIDT SUBSPACE THEOREM 392 7.5.1 SUBSPACE THEOREM 392 7.5.2
PROOF OF SUBSPACE THEOREM 395 7.6 CARTAN'S METHOD 399 7.7 SUBSPACE
THEOREMS ON HYPERSURFACES 403 7.7.1 STATEMENTS OF THEOREMS 404 7.7.2
PROOF OF THEOREM 7.35 406 VOJTA'S CONJECTURES 415 8.1 MORDELLIC
VARIETIES 415 8.2 MAIN CONJECTURE 420 8.3 GENERAL CONJECTURE 424 8.4
VOJTA'S (L,L)-FORM CONJECTURE 429 8.5 A&C-CONJECTURE IMPLIES VOJTA'S
HEIGHT INEQUALITY 432 I-FUNCTIONS 434 9.1 DIRICHLET SERIES 434 9.1.1
ABSCISSA OF CONVERGENCE 434 9.1.2 RIEMANN'S -FUNCTION 436 9.1.3
DIRICHLET' CONTENTS XI 9.2.1 THE C-FUNCTIONS OF NUMBER FIELDS 454 9.2.2
SEIBERG CLASS 456 9.3 SPECIAL LINEAR GROUPS 459 9.3.1 GENERAL LINEAR
GROUPS 459 9.3.2 MODULAR GROUPS 461 9.4 MODULAR FUNCTIONS 464 9.4.1
AUTOMORPHIC FORMS 464 9.4.2 WEIERSTRASS P FUNCTION 466 9.4.3 ELLIPTIC
MODULAR FUNCTIONS 468 9.4.4 HECKE'S THEOREM 470 9.5 MODULAR FORMS 475
9.5.1 MODULAR FORMS FOR SL(2, Z) 475 9.5.2 MODULAR FORMS FOR CONGRUENCE
SUBGROUPS 478 9.5.3 HECKE OPERATOR 480 9.5.4 HECKE'S L-SERIES 483 9.5.5
MODULAR REPRESENTATIONS 484 9.6 HASSE-WEIL L-FUNCTIONS 485 9.7
L-FUNCTIONS OF VARIETIES 490 9.7.1 L-FUNCTIONS OFP N 492 9.7.2
L-FUNCTIONS OF ABELIAN VARIETIES 493 BIBLIOGRAPHY 495 SYMBOLS 511 INDEX
515 |
| any_adam_object | 1 |
| author | Hu, Pei-Chu 1961- Yang, Chung-Chun 1942- |
| author_GND | (DE-588)131783211 (DE-588)131783238 |
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| dewey-full | 512.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 |
| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-20T10:02:52Z |
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| isbn | 9783110205367 |
| language | English |
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| physical | XI, 527 S. |
| publishDate | 2008 |
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| publisher | Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Hu, Pei-Chu 1961- Verfasser (DE-588)131783211 aut Distribution theory of algebraic numbers by Pei-Chu Hu and Chung-Chun Yang Berlin [u.a.] Gruyter 2008 XI, 527 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 45 Diophantine approximation Nevanlinna theory Algebraische Zahl (DE-588)4141847-5 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Körpererweiterung (DE-588)4164435-9 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Diophantische Approximation (DE-588)4135760-7 s Körpererweiterung (DE-588)4164435-9 s Algebraische Zahl (DE-588)4141847-5 s DE-604 Yang, Chung-Chun 1942- Verfasser (DE-588)131783238 aut De Gruyter expositions in mathematics 45 (DE-604)BV004069300 45 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3147705&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017114671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hu, Pei-Chu 1961- Yang, Chung-Chun 1942- Distribution theory of algebraic numbers De Gruyter expositions in mathematics Diophantine approximation Nevanlinna theory Algebraische Zahl (DE-588)4141847-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Körpererweiterung (DE-588)4164435-9 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| subject_GND | (DE-588)4141847-5 (DE-588)4067277-3 (DE-588)4164435-9 (DE-588)4135760-7 |
| title | Distribution theory of algebraic numbers |
| title_auth | Distribution theory of algebraic numbers |
| title_exact_search | Distribution theory of algebraic numbers |
| title_full | Distribution theory of algebraic numbers by Pei-Chu Hu and Chung-Chun Yang |
| title_fullStr | Distribution theory of algebraic numbers by Pei-Chu Hu and Chung-Chun Yang |
| title_full_unstemmed | Distribution theory of algebraic numbers by Pei-Chu Hu and Chung-Chun Yang |
| title_short | Distribution theory of algebraic numbers |
| title_sort | distribution theory of algebraic numbers |
| topic | Diophantine approximation Nevanlinna theory Algebraische Zahl (DE-588)4141847-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Körpererweiterung (DE-588)4164435-9 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| topic_facet | Diophantine approximation Nevanlinna theory Algebraische Zahl Zahlentheorie Körpererweiterung Diophantische Approximation |
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| volume_link | (DE-604)BV004069300 |
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