Diophantine Approximations
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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
Introduction To Diophantine Approximations
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-06-29
Introduction To Diophantine Approximations written by Serge Lang 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 1995-06-29 with Mathematics categories.
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 Approximations
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Author : Ivan Morton Niven
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Diophantine Approximations written by Ivan Morton 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 2008-01-01 with Mathematics categories.
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts. The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discussion. Each chapter concludes with a bibliographic account of closely related work; these sections also contain the sources from which the proofs are drawn.
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 Approximations And Value Distribution Theory
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Author : Paul Alan Vojta
language : en
Publisher: Springer
Release Date : 2006-11-15
Diophantine Approximations And Value Distribution Theory written by Paul Alan Vojta 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.
Nevanlinna Theory And Its Relation To Diophantine Approximation
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Author : Min Ru
language : en
Publisher: World Scientific
Release Date : 2001-06-06
Nevanlinna Theory And Its Relation To Diophantine Approximation written by Min Ru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-06 with Mathematics categories.
It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects.Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems.
Diophantine Geometry
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Author : Marc Hindry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Diophantine Geometry written by Marc Hindry 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 2013-12-01 with Mathematics categories.
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 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.
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.
Lecture Notes On Diophantine Analysis
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Author : Umberto Zannier
language : en
Publisher: Springer
Release Date : 2015-05-05
Lecture Notes On Diophantine Analysis 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 2015-05-05 with Mathematics categories.
These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.