On Some Applications Of Diophantine Approximations
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On Some Applications Of Diophantine Approximations
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Author : Umberto Zannier
language : en
Publisher: Springer
Release Date : 2015-02-13
On Some Applications Of Diophantine Approximations written by Umberto Zannier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-13 with Mathematics categories.
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.
Some Applications Of Diophantine Approximation To Diophantine Equations With Special Emphasis On The Schmidt Subspace Theorem
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Author : Umberto Zannier
language : en
Publisher:
Release Date : 2003
Some Applications Of Diophantine Approximation To Diophantine Equations With Special Emphasis On The Schmidt Subspace Theorem written by Umberto Zannier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
On Some Applications Of Diophantine Approximations
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Author : Carl Ludwig Siegel
language : en
Publisher:
Release Date : 2014
On Some Applications Of Diophantine Approximations written by Carl Ludwig Siegel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Diophantine analysis categories.
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.
Diophantine Approximation And Its Applications
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Author : Charles F. Osgood
language : en
Publisher:
Release Date : 1973
Diophantine Approximation And Its Applications written by Charles F. Osgood and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
This volume represents the proceedings of a Conference on Diophantine Approximation and Its Applications held in Washington, D.C., June 6-8, 1972, and sponsored by the Mathematics Research Center of the Naval Research Laboratory. The purpose of this meeting was to stimulate research in the area of Diophantine approximation by bringing together many of the leading researchers in this field so that they could exchange information and ideas. Fourteen formal lectures were presented at the conference, and these are the papers contained in this volume.
Applications Of Diophantine Approximation To Integral Points And Transcendence
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Author : Pietro Corvaja
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-03
Applications Of Diophantine Approximation To Integral Points And Transcendence written by Pietro Corvaja and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-03 with Mathematics categories.
Introduction to Diophantine approximation and equations focusing on Schmidt's subspace theorem, with applications to transcendence.
Diophantine Approximations And Diophantine Equations
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Author : Wolfgang M. Schmidt
language : en
Publisher: Springer
Release Date : 2006-12-08
Diophantine Approximations And Diophantine Equations written by Wolfgang M. Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
"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
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Author : Ivan Niven
language : en
Publisher: Courier Corporation
Release Date : 2013-01-23
Diophantine Approximations written by Ivan Niven and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-23 with Mathematics categories.
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
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Author : David Masser
language : en
Publisher: Springer
Release Date : 2008-02-01
Diophantine Approximation written by David Masser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-01 with Mathematics categories.
Diophantine Approximation is a branch of Number Theory having its origins intheproblemofproducing“best”rationalapproximationstogivenrealn- bers. Since the early work of Lagrange on Pell’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and - terest, the theory can have fundamental applications to classical diophantine problems in Number Theory. During the whole 20th century, until very recent times, this fruitful interplay went much further, also involving Transcend- tal Number Theory and leading to the solution of several central conjectures on diophantine equations and class number, and to other important achie- ments. These developments naturally raised further intensive research, so at the moment the subject is a most lively one. This motivated our proposal for a C. I. M. E. session, with the aim to make it available to a public wider than specialists an overview of the subject, with special emphasis on modern advances and techniques. Our project was kindly supported by the C. I. M. E. Committee and met with the interest of a largenumberofapplicants;forty-twoparticipantsfromseveralcountries,both graduatestudentsandseniormathematicians,intensivelyfollowedcoursesand seminars in a friendly and co-operative atmosphere. The main part of the session was arranged in four six-hours courses by Professors D. Masser (Basel), H. P. Schlickewei (Marburg), W. M. Schmidt (Boulder) and M. Waldschmidt (Paris VI). This volume contains expanded notes by the authors of the four courses, together with a paper by Professor Yu. V.
Diophantine Analysis
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Author : Jorn Steuding
language : en
Publisher: CRC Press
Release Date : 2005-05-19
Diophantine Analysis written by Jorn Steuding and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-19 with Mathematics categories.
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 approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers. Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.
Diophantine Approximation
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Author : W.M. Schmidt
language : en
Publisher: Springer
Release Date : 2009-02-05
Diophantine Approximation written by W.M. Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-05 with Mathematics categories.
"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)