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Diophantine Approximation

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Author(s): Lukas Pottmeyer
Series: lecture notes
Edition: version 2022-01-17
Year: 2022

Language: German
Commentary: Downloaded from https://web.archive.org/web/20220330222301/https://www.uni-due.de/~adg350u/Skripte/DioApp.pdf

Foundations
Introduction to Diophantine Approximations
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions and Pell's Equation
The Weil-Height
The Mahler Measure
Recap on Valuation Theory
The Weil-height (finally)
Siegel's Lemma
On Lehmer's Conjecture
Siegel's Lemma Once More
Roth's Theorem
Thue equations
Preliminaries I – Multivariable Polynomial Estimates
Preliminaries II – Linearly Independent Polynomials
Preliminaries III – Roth's Lemma
The Proof
Generalizations
Linear Forms in Logarithms
The Gelfond-Schneider Theorem
Applications