Cart
Free US shipping over $10
Proud to be B-Corp

Introduction to Diophantine Approximations Serge Lang

Introduction to Diophantine Approximations By Serge Lang

Introduction to Diophantine Approximations by Serge Lang


$139.39
Condition - New
Only 2 left

Summary

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;

Introduction to Diophantine Approximations Summary

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 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.

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.

Additional information

NPB9780387944562
9780387944562
0387944567
Introduction to Diophantine Approximations: New Expanded Edition by Serge Lang
New
Hardback
Springer-Verlag New York Inc.
1995-06-29
130
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Customer Reviews - Introduction to Diophantine Approximations