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＜電子ブック＞
Introduction to Diophantine Approximations : New Expanded Edition / by Serge Lang

版	2nd ed. 1995.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1995
本文言語	英語
大きさ	X, 130 p : online resource
著者標目	*Lang, Serge author SpringerLink (Online service)
件　名	LCSH:Number theory FREE:Number Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-1-4612-4220-8

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