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" Introduction to Diophantine Approximations "
by Serge Lang.
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BL
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| Record Number
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573751
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b402970
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| Main Entry
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Lang, Serge.
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| Title & Author
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Introduction to Diophantine Approximations : New Expanded Edition /\ by Serge Lang.
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| Publication Statement
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New York, NY :: Springer New York,, 1995.
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| ISBN
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9781461242208
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: 9781461287001
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| Contents
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I General Formalism -- {sect}1. Rational Continued Functions -- {sect}2. The Continued Fraction of a Real Number -- {sect}3. Equivalent Numbers -- {sect}4. Intermediate Convergents -- II Asymptotic Approximations -- {sect}1. Distribution of the Convergents -- {sect}2. Numbers of Constant Type -- {sect}3. Asymptotic Approximations -- {sect}4. Relation with Continued Fractions -- III Estimates of Averaging Sums -- {sect}1. The Sum of the Remainders -- {sect}2. The Sum of the Reciprocals -- {sect}3. Quadratic Exponential Sums -- {sect}4. Sums with More General Functions -- IV Quadratic Irrationalities -- {sect}1. Quadratic Numbers and Periodicity -- {sect}2. Units and Continued Fractions -- {sect}3. The Basic Asymptotic Estimate -- V The Exponential Function -- {sect}1. Some Continued Functions -- {sect}2. The Continued Fraction for e -- {sect}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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| Abstract
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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.
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Mathematics.
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Number theory.
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SpringerLink (Online service)
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