Introduction to Diophantine Approximations
Introduction to Diophantine Approximations

Author: Serge Lang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 138

ISBN-13: 1461242207

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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.

Diophantine Approximation on Linear Algebraic Groups
Diophantine Approximation on Linear Algebraic Groups

Author: Michel Waldschmidt

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 649

ISBN-13: 3662115697

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The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

Diophantine Geometry
Diophantine Geometry

Author: Marc Hindry

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 574

ISBN-13: 1461212103

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This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Diophantine Approximation
Diophantine Approximation

Author: W.M. Schmidt

Publisher: Springer

Published: 2009-02-05

Total Pages: 312

ISBN-13: 3540386459

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"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

Diophantine Approximations
Diophantine Approximations

Author: Ivan Niven

Publisher: Courier Corporation

Published: 2013-01-23

Total Pages: 82

ISBN-13: 0486164705

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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.

Distribution Modulo One and Diophantine Approximation
Distribution Modulo One and Diophantine Approximation

Author: Yann Bugeaud

Publisher: Cambridge University Press

Published: 2012-07-05

Total Pages: 317

ISBN-13: 0521111692

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A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.