Details

Autor(en) / Beteiligte

• Lang, Serge,

Titel

Introduction to diophantine approximations

Auflage

New expanded edition

Ort / Verlag

New York : Springer-Verlag,

Erscheinungsjahr

[1995]

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Originally published: Reading, Mass. : Addison-Wesley Pub. Co., 1966. Addison-Wesley series in mathematics.
• Includes bibliographical references (pages [79]-80) and index.
• 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.
• 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.
• English
• Description based on print version record.