Diophantine Approximation

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