Front cover image for Introduction to diophantine approximations

Introduction to diophantine approximations

Serge Lang
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;
eBook, English, ©1995
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Springer-Verlag, New York, ©1995
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9780387944562, 0387944567
1012458261
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.
Originally published: Reading, Mass. : Addison-Wesley Pub. Co., 1966. Addison-Wesley series in mathematics
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