Diophantine approximation: lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Series: | Lecture notes in mathematics
1819 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 351 S. |
| ISBN: | 3540403922 |
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| 245 | 1 | 0 | |a Diophantine approximation |b lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 |c Fondazione CIME. D. Masser ... Ed.: F. Amoroso ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XI, 351 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1819 | |
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Record in the Search Index
| _version_ | 1804130144911097856 |
|---|---|
| adam_text | Contents
Heights, Transcendence, and
Linear
Independence on
Commutative Group Varieties
David
Masser................................................... 1
1
First lecture. Introduction and basic techniques
.................. 1
2
Second lecture. More on heights
................................ 8
3
Third lecture. Elliptic functions and elliptic curves
................ 17
4
Fourth lecture. Linear forms in elliptic logarithms
................ 24
5
Fifth lecture. Abelian varieties
................................. 32
6
Sixth Lecture. Commutative group varieties
..................... 39
References
...................................................... 47
Linear Forms in Logarithms of Rational Numbers
Yuri Nesterenko
................................................. 53
1
Introduction
................................................. 53
2
Main result and induction assumption
.......................... 54
3
Construction of auxiliary function
.............................. 59
3.1
Binomial polynomial
..................................... 59
3.2
Siegeľs
lemma with weights
............................... 62
3.3
Some topics from the geometry of numbers
.................. 66
3.4
Upper bound for an index
................................ 69
3.5
Construction
............................................ 71
4
Extrapolation of zeros
........................................ 79
4.1
Interpolation formula
..................................... 81
4.2
Extrapolation of zeros in
Q
............................... 83
4.3
Extrapolation with
Kummer
descent
....................... 90
5
Zero estimates and the end of the proof of Theorem
2.1........... 95
5.1
Zero estimates on linear algebraic groups
................... 97
5.2
Construction of the
sublattice
Φ
from Proposition
2.6........ 98
References
......................................................106
X
Contents
Approximation
of Algebraic Numbers
Hans Peter Schlickewei
...........................................107
1
Results
......................................................107
2
Roth s proof of theorem
1.1....................................112
2.1
Vanishing
...............................................113
2.2
Non-
Vanishing
..........................................116
2.3
Conclusion
..............................................117
3
Schmidt s proof of theorem
1.2.................................118
3.1
Parallelepipeds
..........................................118
3.2
The approximation part
..................................120
3.3
The geometry part
.......................................127
4
The proof of theorem
1.3......................................130
4.1
Parallelepipeds
..........................................131
4.2
The approximation part
..................................135
4.3
The geometry part
.......................................137
5
Generalization of theorem
1.4..................................144
5.1
Parallelepipeds
..........................................146
5.2
The approximation part
..................................150
6
Gap principles
...............................................161
6.1
Vanishing determinants
...................................161
6.2
Application of Minkowski s Theorem
.......................166
References
......................................................170
Linear Recurrence Sequences
Wolfgang M. Schmidt
.............................................171
1
Introduction
.................................................171
2
Functions of Polynomial-Exponential Type
......................173
3
Generating Functions
.........................................179
4
Factorization of Polynomial-Exponential Functions
...............180
5
Gourin s Theorem
............................................185
6
Hadamard
Products, Quotients and Roots
.......................190
7
The Zero-Multiplicity, and Polynomial-Exponential Equations
......192
8
Proof of Laurent s Theorem in the Number Field Case
............195
9
A Specialization Argument
....................................200
10
A Method of Zannier Using Derivations
.........................202
11
Applications to Linear Recurrences
.............................207
12
Bounds for the Number of Solutions of Polynomial-Exponential
Equations
...................................................213
13
The
Bavencoffe-Bézivin
Sequence
...............................218
14
Proof of Evertse s Theorem on Roots of Unity
...................223
15
Reductions for Theorem
12.3 ..................................226
16
Special Solutions
.............................................229
17
Properties of Special Solutions
.................................231
18
Large Solutions
..............................................234
19
Small Solutions, and the end of the proof of Theorem
12.3.........235
Contents
XI
20 Linear
Recurrence Sequences Again
.............................236
21
Final Remarks
...............................................243
References
......................................................245
Linear Independence Measures for Logarithms of Algebraic
Numbers
Michel
Waldschmidt..............................................249
1
First Lecture. Introduction to Transcendence Proofs
..............252
1.1
Sketch of Proof
..........................................252
1.2
Tools for the Auxiliary Function
...........................253
1.3
Proof with an Auxiliary Function and without Zero Estimate.
. 255
1.4
Tools for the Interpolation Determinant Method
.............260
1.5
Proof with an Interpolation Determinant and a Zero Estimate
. 261
1.6
Remarks
................................................262
2
Second Lecture. Extrapolation with Interpolation Determinants
.... 267
2.1
Upper Bound for a Determinant in a Single Variable
.........267
2.2
Proof of Hermite-Lindemann s Theorem with an Interpolation
Determinant and without Zero Estimate
....................273
3
Third Lecture. Linear Independence of Logarithms of Algebraic
Numbers
....................................................277
3.1
Introduction to Baker s Method
...........................278
3.2
Proof of Baker s Theorem
.................................283
3.3
Further Extrapolation with the Auxiliary Function
...........289
3.4
Upper Bound for a Determinant in Several Variables
.........291
3.5
Extrapolation with an Interpolation Determinant
............297
4
Fourth Lecture. Introduction to Diophantine Approximation
.......300
4.1
On a Conjecture of Mahler
................................300
4.2
Fel dman s Polynomials
...................................306
4.3
Output of the Transcendence Argument
....................307
4.4
From Polynomial Approximation to Algebraic Approximation
. 312
4.5
Proof of Theorem
4.2.....................................315
5
Fifth Lecture. Measures of Linear Independence of Logarithms of
Algebraic Numbers
...........................................316
5.1
Introduction
............................................316
5.2
Baker s Method with an Auxiliary Function
................318
6
Sixth Lecture. Matveev s Theorem with Interpolation Determinants
336
6.1
First Extrapolation
......................................337
6.2
Using Kummer s Condition
...............................338
6.3
Second Extrapolation
....................................340
6.4
An Approximate
Schwarz
Lemma for Interpolation
Determinants
...........................................341
References
......................................................342
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| spelling | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 Fondazione CIME. D. Masser ... Ed.: F. Amoroso ... Berlin [u.a.] Springer 2003 XI, 351 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1819 Literaturangaben Approximation diophantienne - Congrès Approximation diophantienne rasuqam Nombre entier algébrique rasuqam Diophantine approximation Congresses Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2000 Cetraro gnd-content Diophantische Approximation (DE-588)4135760-7 s DE-604 Masser, David William 1948- Sonstige (DE-588)102371499X oth Amoroso, Francesco Sonstige oth Lecture notes in mathematics 1819 (DE-604)BV000676446 1819 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010430101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 Lecture notes in mathematics Approximation diophantienne - Congrès Approximation diophantienne rasuqam Nombre entier algébrique rasuqam Diophantine approximation Congresses Diophantische Approximation (DE-588)4135760-7 gnd |
| subject_GND | (DE-588)4135760-7 (DE-588)1071861417 |
| title | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 |
| title_auth | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 |
| title_exact_search | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 |
| title_full | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 Fondazione CIME. D. Masser ... Ed.: F. Amoroso ... |
| title_fullStr | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 Fondazione CIME. D. Masser ... Ed.: F. Amoroso ... |
| title_full_unstemmed | Diophantine approximation lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 Fondazione CIME. D. Masser ... Ed.: F. Amoroso ... |
| title_short | Diophantine approximation |
| title_sort | diophantine approximation lectures given at the cime summer school held in cetraro italy june 28 july 6 2000 |
| title_sub | lectures given at the CIME summer school held in Cetraro , Italy, June 28 - July 6, 2000 |
| topic | Approximation diophantienne - Congrès Approximation diophantienne rasuqam Nombre entier algébrique rasuqam Diophantine approximation Congresses Diophantische Approximation (DE-588)4135760-7 gnd |
| topic_facet | Approximation diophantienne - Congrès Approximation diophantienne Nombre entier algébrique Diophantine approximation Congresses Diophantische Approximation Konferenzschrift 2000 Cetraro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010430101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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