Diophantine Approximations and Diophantine Equations
Title | Diophantine Approximations and Diophantine Equations PDF eBook |
Author | Wolfgang M. Schmidt |
Publisher | Springer |
Pages | 224 |
Release | 2006-12-08 |
Genre | Mathematics |
ISBN | 3540473742 |
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Introduction to Diophantine Approximations
Title | Introduction to Diophantine Approximations PDF eBook |
Author | Serge Lang |
Publisher | Springer Science & Business Media |
Pages | 138 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461242207 |
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.
An Introduction to Diophantine Approximation
Title | An Introduction to Diophantine Approximation PDF eBook |
Author | John William Scott Cassels |
Publisher | |
Pages | 180 |
Release | 1957 |
Genre | Diophantine analysis |
ISBN |
Diophantine Approximations
Title | Diophantine Approximations PDF eBook |
Author | Ivan Niven |
Publisher | Courier Corporation |
Pages | 82 |
Release | 2013-01-23 |
Genre | Mathematics |
ISBN | 0486164705 |
This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of complex numbers, and product of complex linear forms. 1963 edition.
Diophantine Approximation
Title | Diophantine Approximation PDF eBook |
Author | Robert F. Tichy |
Publisher | Springer Science & Business Media |
Pages | 416 |
Release | 2008-07-10 |
Genre | Mathematics |
ISBN | 3211742808 |
This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schrödinger-Institute (Vienna, 2003). The articles are either in the spirit of more classical diophantine analysis or of a geometric or combinatorial flavor. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials.
Diophantine Analysis
Title | Diophantine Analysis PDF eBook |
Author | Jorn Steuding |
Publisher | CRC Press |
Pages | 271 |
Release | 2005-05-19 |
Genre | Mathematics |
ISBN | 1420057200 |
While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine ap
Diophantine Approximation and Abelian Varieties
Title | Diophantine Approximation and Abelian Varieties PDF eBook |
Author | Bas Edixhoven |
Publisher | Springer |
Pages | 136 |
Release | 2009-02-05 |
Genre | Mathematics |
ISBN | 3540482083 |
The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper "Diophantine approximation on abelian varieties", Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.