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Field name	Details
Dewey Class	512.7
Title	Introduction to Diophantine Approximations ([EBook] :) : New Expanded Edition / by Serge Lang.
Author	Lang, Serge. , 1927-2005
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1995.
Physical Details	X, 130 pages : online resource.
ISBN	9781461242208
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-4220-8
Links to Related Works	Subject References: Mathematics . Number Theory . Authors: Lang, Serge. 1927-2005 . Lang, Serge, 1927-2005. . Corporate Authors: SpringerLink (Online service) . Classification: 512.7 .

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Introduction to Diophantine Approximations

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