Introduction to Diophantine Approximations: New Expanded EditionSpringer 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. |
Table des matières
| 1 | |
4 Intermediate Convergents | 17 |
CHAPTER V | 31 |
4 Relation with Continued Fractions | 33 |
4 Sums with More General Functions | 47 |
3 The Basic Asymptotic Estimate | 63 |
The Exponential Function | 69 |
55 | 88 |
APPENDIX | 93 |
APPENDIX C | 126 |
Autres éditions - Tout afficher
Introduction to Diophantine Approximations: New Expanded Edition Serge Lang Aucun aperçu disponible - 2013 |
Introduction to Diophantine Approximations: New Expanded Edition Serge Lang Aucun aperçu disponible - 2012 |
Expressions et termes fréquents
a₁ a₂ absolute value algebraic integer algebraic numbers an+1 an+2 assume asymptotic estimate bounded ce² Chapter computations condition constant type Corollary define determine diophantine approximations discriminant dv² equivalent error term estimate of Theorem exponential sums finite number follows Fourier coefficients Fourier series Hence induction inequality qa integer coefficients integers q inverse function irrational number Lemma Math number of integers number of solutions obtain p/q and p'/q partial quotients Periodical continued fractions Pn/qn polynomial positive integer positive units principal convergents principal cotype g proves our theorem purely periodic q sufficiently quadratic equation quadratic irrational quadratic numbers R(na rational number real number reduced relatively prime relatively prime integers Root of x3 satisfying sequence SERGE LANG set of numbers specific numbers sufficiently large sufficiently small thereby proving w₁ whence write απ