Diophantine Approximation And Transcendence Theory
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Diophantine Approximation And Transcendence Theory
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Author : Gisbert Wustholz
language : en
Publisher:
Release Date : 2014-01-15
Diophantine Approximation And Transcendence Theory written by Gisbert Wustholz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Diophantine Approximation On Linear Algebraic Groups
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Author : Michel Waldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Diophantine Approximation On Linear Algebraic Groups written by Michel Waldschmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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 Approximation And Transcendence Theory
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Author : Gisbert Wüstholz
language : en
Publisher: Springer
Release Date : 2006-11-15
Diophantine Approximation And Transcendence Theory written by Gisbert Wüstholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Classical Diophantine Equations
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Author : Vladimir G. Sprindzuk
language : en
Publisher: Springer
Release Date : 2006-11-15
Classical Diophantine Equations written by Vladimir G. Sprindzuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.
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 ap
Distribution Modulo One And Diophantine Approximation
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Author : Yann Bugeaud
language : en
Publisher: Cambridge University Press
Release Date : 2012-07-05
Distribution Modulo One And Diophantine Approximation written by Yann Bugeaud 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 2012-07-05 with Mathematics categories.
This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references.
A Panorama Of Number Theory Or The View From Baker S Garden
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Author : Gisbert Wüstholz
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-26
A Panorama Of Number Theory Or The View From Baker S Garden written by Gisbert Wüstholz 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 2002-09-26 with Mathematics categories.
This is a selection of high quality articles on number theory by leading figures.
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 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 Approximation
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Author : Wolfgang M. Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 1970
Diophantine Approximation written by Wolfgang M. Schmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Diophantine analysis categories.