Classical diophantine equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1559 : Subseries LOMI and Euler International Mathematical Institute, St. Petersburg |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XI, 228 S. |
| ISBN: | 3540573593 0387573593 |
Internformat
MARC
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| 100 | 1 | |a Sprindžuk, Vladimir G. |d 1936-1987 |e Verfasser |0 (DE-588)113603673 |4 aut | |
| 240 | 1 | 0 | |a Klassičeskie diofantovye uravnenija ot dvych neizvestnych |
| 245 | 1 | 0 | |a Classical diophantine equations |c Vladimir G. Sprindžuk |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XI, 228 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1559 : Subseries LOMI and Euler International Mathematical Institute, St. Petersburg | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents
I. Origins 1
1.1 Runge s Theorem 1
1.2 Liouville s Inequality; the Theorem and Method of Thue 3
1.3 Exponential Equations and Skolera s Method 7
1.4 Hilbert s Seventh Problem and its Development 10
II. Algebraic Foundations 14
II. 1 Height and Size of an Algebraic Number 14
112 Bounds for Units, Regulators and Class Numbers 17
II.3 Analytic Functions in p adic Fields 22
III. Linear Forms in the Logarithms of Algebraic Numbers 30
III. 1 Direct Bounds and Connections
Between Bounds in Different Metrics 30
111.2 Preliminary Facts 32
111.3 The Auxiliary System of Linear Equations 36
111.4 Transition to the Auxiliary Function 39
III. 5 Analytic arithmetical Extrapolation 43
III.6 Completion of the Proof of Lemma 1.1 46
III. 7 Connection Between Bounds
in Different Non archimedean Metrics 53
III.8 Lemmas on Direct Bounds 58
IV. The Thue Equation 61
IV. 1 Existence of a Computable Bound for Solutions 61
IV.2 Dependence on the Number Represented by the Form 64
IV.3 Exceptional Forms 70
IV.4 Estimates for the Solutions in terms of the Main Parameters 73
IV.5 Norm Forms with Two Dominating Variables 75
IV.6 Equations in Relative Fields 80
V. The Thue Mahler Equation 85
V.I Solution of the Thue Equation in S integers 85
XI
V.2 Rational Approximation to Algebraic Numbers
in Several Metrics 92
V.3 The Greatest Prime Factor of a Binary Form 94
V.4 The Generalised Thue Mahler Equation 98
V.5 Approximations to Algebraic
Numbers by Algebraic Numbers of Fixed Field 105
VI. Elliptic and Hyperelliptic Equations Ill
VI. 1 The Simplest Elliptic Equations Ill
VI.2 The General Hyperelliptic Equation 116
VI.3 Linear Dependence of Three Algebraic Units 118
VI.4 Main Theorem 120
VI.5 Estimate for the Number of Solutions 125
VI.6 Linear Dependence of Three S units 126
VI.7 Solutions in S integers 131
VI.8 5 integer Points on Elliptic Curves 133
VII. Equations of Hyperelliptic Type 138
VII. 1 Equations with Fixed Exponent 138
VII.2 Equations with indefinite exponent 144
VII.3 The Catalan Equation 148
VIII. The Class Number Value Problem 155
VIII. 1 Influence of the Value of the Class Number
on the Size of the Solutions 155
VIII.2 Real Quadratic Fields 159
VIII.3 Fields of Degree 3,4 and 6 163
VIII.4 Superposition of Polynomials 167
VIII. 5 The Ankeny Brauer Chowla Fields 170
VIII.6 A Statistical Approach 176
VIII. 7 Conjectures and Perspectives 184
IX. Reducibility of Polynomials and Diophantine Equations 188
IX. 1 An Irreducibility Theorem of Hilbert s Type 188
IX.2 Main argument 191
IX.3 Details and Sharpenings 197
IX.4 Theorems on Reducibility 205
IX.5 Proofs of the Reducibility Theorems 208
IX.6 Further Results and Remarks 213
References 219
|
| any_adam_object | 1 |
| author | Sprindžuk, Vladimir G. 1936-1987 |
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| discipline | Mathematik |
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| id | DE-604.BV008331938 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:18:27Z |
| institution | BVB |
| isbn | 3540573593 0387573593 |
| language | English |
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| physical | XI, 228 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Sprindžuk, Vladimir G. 1936-1987 Verfasser (DE-588)113603673 aut Klassičeskie diofantovye uravnenija ot dvych neizvestnych Classical diophantine equations Vladimir G. Sprindžuk Berlin [u.a.] Springer 1993 XI, 228 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1559 : Subseries LOMI and Euler International Mathematical Institute, St. Petersburg Aus dem Russ. übers. Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 s DE-604 Lecture notes in mathematics 1559 : Subseries LOMI and Euler International Mathematical Institute, St. Petersburg (DE-604)BV000676446 1559 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005504232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sprindžuk, Vladimir G. 1936-1987 Classical diophantine equations Lecture notes in mathematics Diophantische Gleichung (DE-588)4012386-8 gnd |
| subject_GND | (DE-588)4012386-8 |
| title | Classical diophantine equations |
| title_alt | Klassičeskie diofantovye uravnenija ot dvych neizvestnych |
| title_auth | Classical diophantine equations |
| title_exact_search | Classical diophantine equations |
| title_full | Classical diophantine equations Vladimir G. Sprindžuk |
| title_fullStr | Classical diophantine equations Vladimir G. Sprindžuk |
| title_full_unstemmed | Classical diophantine equations Vladimir G. Sprindžuk |
| title_short | Classical diophantine equations |
| title_sort | classical diophantine equations |
| topic | Diophantische Gleichung (DE-588)4012386-8 gnd |
| topic_facet | Diophantische Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005504232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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