Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorLang, Serge. author
TitleIntroduction to Diophantine Approximations [electronic resource] : New Expanded Edition / by Serge Lang
ImprintNew York, NY : Springer New York, 1995
Connect to
Descript X, 130 p. online resource


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 -- ยง1. Rational Continued Functions -- ยง2. The Continued Fraction of a Real Number -- ยง3. Equivalent Numbers -- ยง4. Intermediate Convergents -- II Asymptotic Approximations -- ยง1. Distribution of the Convergents -- ยง2. Numbers of Constant Type -- ยง3. Asymptotic Approximations -- ยง4. Relation with Continued Fractions -- III Estimates of Averaging Sums -- ยง1. The Sum of the Remainders -- ยง2. The Sum of the Reciprocals -- ยง3. Quadratic Exponential Sums -- ยง4. Sums with More General Functions -- IV Quadratic Irrationalities -- ยง1. Quadratic Numbers and Periodicity -- ยง2. Units and Continued Fractions -- ยง3. The Basic Asymptotic Estimate -- V The Exponential Function -- ยง1. Some Continued Functions -- ยง2. The Continued Fraction for e -- ยง3. 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

Mathematics Number theory Mathematics Number Theory


Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network


facebook   instragram