Diophantine Analysis

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Diophantine Analysis

Author : Jörn Steuding
Publisher : Birkhäuser
ISBN 13 : 3319488171
Total Pages : 239 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Diophantine Analysis by : Jörn Steuding

Download or read book Diophantine Analysis written by Jörn Steuding and published by Birkhäuser. This book was released on 2016-12-21 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.

Elliptic Curves

Author : S. Lang
Publisher : Springer Science & Business Media
ISBN 13 : 3662070103
Total Pages : 270 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Elliptic Curves by : S. Lang

Download or read book Elliptic Curves written by S. Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.

Exploring the Number Jungle: A Journey into Diophantine Analysis

Author : Edward B. Burger
Publisher : American Mathematical Soc.
ISBN 13 : 0821826409
Total Pages : 160 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Exploring the Number Jungle: A Journey into Diophantine Analysis by : Edward B. Burger

Download or read book Exploring the Number Jungle: A Journey into Diophantine Analysis written by Edward B. Burger and published by American Mathematical Soc.. This book was released on 2000 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory."--BOOK JACKET.

Diophantine Analysis

Author : Robert Daniel Carmichael
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Diophantine Analysis by : Robert Daniel Carmichael

Download or read book Diophantine Analysis written by Robert Daniel Carmichael and published by . This book was released on 1915 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lecture Notes on Diophantine Analysis

Author : Umberto Zannier
Publisher : Springer
ISBN 13 : 8876425179
Total Pages : 248 pages
Book Rating : 4.8/5 (764 download)

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Book Synopsis Lecture Notes on Diophantine Analysis by : Umberto Zannier

Download or read book Lecture Notes on Diophantine Analysis written by Umberto Zannier and published by Springer. This book was released on 2015-05-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Diophantine Approximations and Diophantine Equations

Author : Wolfgang M. Schmidt
Publisher : Springer
ISBN 13 : 3540473742
Total Pages : 224 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Diophantine Approximations and Diophantine Equations by : Wolfgang M. Schmidt

Download or read book Diophantine Approximations and Diophantine Equations written by Wolfgang M. Schmidt and published by Springer. This book was released on 2006-12-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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

An Introduction to Diophantine Equations

Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 0817645497
Total Pages : 350 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis An Introduction to Diophantine Equations by : Titu Andreescu

Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory

Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 0387499237
Total Pages : 673 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Number Theory by : Henri Cohen

Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2008-10-10 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Quadratic Diophantine Equations

Author : Titu Andreescu
Publisher : Springer
ISBN 13 : 0387541098
Total Pages : 224 pages
Book Rating : 4.3/5 (875 download)

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Book Synopsis Quadratic Diophantine Equations by : Titu Andreescu

Download or read book Quadratic Diophantine Equations written by Titu Andreescu and published by Springer. This book was released on 2015-06-29 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Diophantus and Diophantine Equations

Author : Isabella Grigoryevna Bashmakova
Publisher : American Mathematical Soc.
ISBN 13 : 1470450488
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Diophantus and Diophantine Equations by : Isabella Grigoryevna Bashmakova

Download or read book Diophantus and Diophantine Equations written by Isabella Grigoryevna Bashmakova and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus—a person whose very existence has long been doubted by most historians of mathematics—will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman, who notes the most recent developments including the proof of Fermat's Last Theorem.

Fundamentals of Diophantine Geometry

Author : S. Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1475718101
Total Pages : 383 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Fundamentals of Diophantine Geometry by : S. Lang

Download or read book Fundamentals of Diophantine Geometry written by S. Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

Elliptic Tales

Author : Avner Ash
Publisher : Princeton University Press
ISBN 13 : 0691151199
Total Pages : 277 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Elliptic Tales by : Avner Ash

Download or read book Elliptic Tales written by Avner Ash and published by Princeton University Press. This book was released on 2012 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture.

Diophantine Geometry

Author : Marc Hindry
Publisher : Springer Science & Business Media
ISBN 13 : 1461212103
Total Pages : 574 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Diophantine Geometry by : Marc Hindry

Download or read book Diophantine Geometry written by Marc Hindry and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Equations and Power Integral Bases

Author : Istvan Gaal
Publisher : Springer Science & Business Media
ISBN 13 : 1461200857
Total Pages : 192 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Diophantine Equations and Power Integral Bases by : Istvan Gaal

Download or read book Diophantine Equations and Power Integral Bases written by Istvan Gaal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Diophantine Approximations

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1461242207
Total Pages : 138 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Diophantine Approximations by : Serge Lang

Download or read book Introduction to Diophantine Approximations written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytic Number Theory and Diophantine Problems

Author : A.C. Adolphson
Publisher : Springer Science & Business Media
ISBN 13 : 9780817633615
Total Pages : 368 pages
Book Rating : 4.6/5 (336 download)

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Book Synopsis Analytic Number Theory and Diophantine Problems by : A.C. Adolphson

Download or read book Analytic Number Theory and Diophantine Problems written by A.C. Adolphson and published by Springer Science & Business Media. This book was released on 1987-01-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A conference on Analytic Number Theory and Diophantine Problems was held from June 24 to July 3, 1984 at the Oklahoma State University in Stillwater. The conference was funded by the National Science Foundation, the College of Arts and Sciences and the Department of Mathematics at Oklahoma State University. The papers in this volume represent only a portion of the many talks given at the conference. The principal speakers were Professors E. Bombieri, P. X. Gallagher, D. Goldfeld, S. Graham, R. Greenberg, H. Halberstam, C. Hooley, H. Iwaniec, D. J. Lewis, D. W. Masser, H. L. Montgomery, A. Selberg, and R. C. Vaughan. Of these, Professors Bombieri, Goldfeld, Masser, and Vaughan gave three lectures each, while Professor Hooley gave two. Special sessions were also held and most participants gave talks of at least twenty minutes each. Prof. P. Sarnak was unable to attend but a paper based on his intended talk is included in this volume. We take this opportunity to thank all participants for their (enthusiastic) support for the conference. Judging from the response, it was deemed a success. As for this volume, I take responsibility for any typographical errors that may occur in the final print. I also apologize for the delay (which was due to the many problems incurred while retyping all the papers). A. special thanks to Dollee Walker for retyping the papers and to Prof. W. H. Jaco for his support, encouragement and hard work in bringing the idea of the conference to fruition.

Diophantine Equations Over Function Fields

Author : R. C. Mason
Publisher : Cambridge University Press
ISBN 13 : 9780521269834
Total Pages : 142 pages
Book Rating : 4.2/5 (698 download)

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Book Synopsis Diophantine Equations Over Function Fields by : R. C. Mason

Download or read book Diophantine Equations Over Function Fields written by R. C. Mason and published by Cambridge University Press. This book was released on 1984-04-26 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of a new approach to the subject.