Introduction to Diophantine Approximations: New Expanded Edition

Couverture
Springer Science & Business Media, 6 déc. 2012 - 130 pages
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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Table des matières

CHAPTER
1
4 Intermediate Convergents
15
CHAPTER V
31
4 Relation with Continued Fractions
32
4 Sums with More General Functions
45
3 The Basic Asymptotic Estimate
61
The Exponential Function
69
APPENDIX
93
APPENDIX C
126
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