Diophantine Approximation

✍ Scribed by Lukas Pottmeyer

Year: 2022
Tongue: German
Leaves: 137
Series: lecture notes
Edition: version 2022-01-17
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

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

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