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Introduction to Diophantine Approximations - Serge Lang

Introduction to Diophantine Approximations

New Expanded Edition

(Autor)

Buch | Hardcover
130 Seiten
1995 | 2nd expanded ed. 1995
Springer-Verlag New York Inc.
978-0-387-94456-2 (ISBN)
CHF 149,75 inkl. MwSt
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; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere.
Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.

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.

Zusatzinfo X, 130 p.
Verlagsort New York, NY
Sprache englisch
Maße 156 x 234 mm
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 0-387-94456-7 / 0387944567
ISBN-13 978-0-387-94456-2 / 9780387944562
Zustand Neuware
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