Lectures on Diophantine Approximations
Kurt Mahler
Notre Dame Mathematical Lectures, Number 7
Notre Dame, Indiana : University of Notre Dame, 1961.
1st
xi+188 pp.
Subjects:
Diophantine analysis10.3010.34
Permanent link to this monograph: http://projecteuclid.org/euclid.ndml/1175197407
Mathmatical Reviews number (MathSciNet):
MR0142509Copyright © 1961, University of Notre Dame.
Title and Copyright Pages
i-iii
Notational Explanations
vii-viii
Part I
Part 1: p-adic and g-adic Numbers, and Their Approximations
1-2
Chapter I: Valuations and Pseudo-valuations
3-25
Chapter II: The p-adic, g-adic, and g*-adic Series
26-40
Chapter III: A Test for Algebraic or Transcendental Numbers
41-57
Chapter IV: Continued Fractions
58-72
Part 2
Part 2: Rational Approximations of Algebraic Numbers. The Problem and Its History
73-76
Chapter V: Roth's Lemma
77-97
Chapter VI: The Approximation Polynomial
98-106
Chapter VII: The First Approximation Theorem
107-132
Chapter VIII: The Second Approximation Theorem
133-146
Chapter IX: Applications
147-162
Appendix A: Another Proof of a Lemma by Schneider
163-168
Appendix B: A Theorem by M. Cugiani
169-180
Appendix C: The Approximation Theorems over Algebraic Number Fields
181-188
