Classical Diophantine Equations
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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over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded.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.
An Introduction To Diophantine Equations
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
An Introduction To Diophantine Equations written by Titu Andreescu 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 2010-09-02 with Mathematics categories.
This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Quadratic Diophantine Equations
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Author : Titu Andreescu
language : en
Publisher: Springer
Release Date : 2015-06-29
Quadratic Diophantine Equations written by Titu Andreescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-29 with Mathematics categories.
This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.
Diophantine Approximation
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Author : Robert F. Tichy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-10
Diophantine Approximation written by Robert F. Tichy 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 2008-07-10 with Mathematics categories.
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.
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 Equations And Power Integral Bases
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Author : István Gaál
language : en
Publisher: Springer Nature
Release Date : 2019-09-03
Diophantine Equations And Power Integral Bases written by István Gaál and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-03 with Mathematics categories.
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Diophantine Equations And Power Integral Bases
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Author : Istvan Gaal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Diophantine Equations And Power Integral Bases written by Istvan Gaal 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 2012-12-06 with Mathematics categories.
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Classical And Modular Methods Applied To Diophantine Equations
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Author : Sander Roland Dahmen
language : en
Publisher:
Release Date : 2008
Classical And Modular Methods Applied To Diophantine Equations written by Sander Roland Dahmen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Neutrosophic Linear Diophantine Equations With Two Variables
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Author : Hasan Sankari
language : en
Publisher: Infinite Study
Release Date : 2020-12-01
Neutrosophic Linear Diophantine Equations With Two Variables written by Hasan Sankari and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Mathematics categories.
This paper is devoted to study for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers. This work introduces an algorithm to solve the linear Diophantine equation.
Classical And Modular Methods Applied To Diophantine Equations
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Author : Sander Roland Dahmen
language : en
Publisher:
Release Date : 2008
Classical And Modular Methods Applied To Diophantine Equations written by Sander Roland Dahmen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.