Introduction to Diophantine Approximations

New Expanded Edition

Häftad, Engelska, 2012

Av Serge Lang

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The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory;

Produktinformation

Utgivningsdatum2012-08-22
Mått155 x 235 x 11 mm
Vikt230 g
FormatHäftad
SpråkEngelska
Antal sidor130
Upplaga2
FörlagSpringer-Verlag New York Inc.
ISBN9781461287001

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I General Formalism.- §1. Rational Continued Functions.- §2. The Continued Fraction of a Real Number.- §3. Equivalent Numbers.- §4. Intermediate Convergents.- II Asymptotic Approximations.- §1. Distribution of the Convergents.- §2. Numbers of Constant Type.- §3. Asymptotic Approximations.- §4. Relation with Continued Fractions.- III Estimates of Averaging Sums.- §1. The Sum of the Remainders.- §2. The Sum of the Reciprocals.- §3. Quadratic Exponential Sums.- §4. Sums with More General Functions.- IV Quadratic Irrationalities.- §1. Quadratic Numbers and Periodicity.- §2. Units and Continued Fractions.- §3. The Basic Asymptotic Estimate.- V The Exponential Function.- §1. Some Continued Functions.- §2. The Continued Fraction for e.- §3. The Basic Asymptotic Estimate.- Appendix A Some Computations in Diophantine Approximations.- Appendix B Continued Fractions for Some Algebraic Numbers.- Appendix C Addendum to Continued Fractions for Some Algebraic Numbers.