Introduction to Diophantine Approximations New Expanded Edition

Introduction to Diophantine Approximations New Expanded Edition / by 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; the determination of these functions for numbers given as classical n...

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Bibliographic Details
Main Author: Lang, Serge (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1995.
Edition:2nd ed. 1995.
Series:Springer eBook Collection.
Subjects:
Number theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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