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Diophantine Approximations and Diophantine Equations

2006-12-08 Mathematics
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Release : 2006-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 742/5 ( reviews)

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Book Synopsis Diophantine Approximations and Diophantine Equations by : Wolfgang M. Schmidt

Download or read book Diophantine Approximations and Diophantine Equations written by Wolfgang M. Schmidt. This book was released on 2006-12-08. Available in PDF, EPUB and Kindle. Book excerpt: "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

Diophantine Approximations

2013-01-23 Mathematics
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Release : 2013-01-23
Genre : Mathematics
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Diophantine Approximations by : Ivan Niven

Download or read book Diophantine Approximations written by Ivan Niven. This book was released on 2013-01-23. Available in PDF, EPUB and Kindle. Book excerpt: 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

2008-07-10 Mathematics
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Release : 2008-07-10
Genre : Mathematics
Kind : eBook
Book Rating : 808/5 ( reviews)

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Book Synopsis Diophantine Approximation by : Robert F. Tichy

Download or read book Diophantine Approximation written by Robert F. Tichy. This book was released on 2008-07-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Diophantine Approximations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 207/5 ( reviews)

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Book Synopsis Introduction to Diophantine Approximations by : Serge Lang

Download or read book Introduction to Diophantine Approximations written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On Some Applications of Diophantine Approximations

2015-02-13 Mathematics
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Release : 2015-02-13
Genre : Mathematics
Kind : eBook
Book Rating : 209/5 ( reviews)

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Book Synopsis On Some Applications of Diophantine Approximations by : Umberto Zannier

Download or read book On Some Applications of Diophantine Approximations written by Umberto Zannier. This book was released on 2015-02-13. Available in PDF, EPUB and Kindle. Book excerpt: This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.

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