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On Some Applications Of Diophantine Approximations
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Book Synopsis On Some Applications of Diophantine Approximations by : Umberto Zannier
Download or read book On Some Applications of Diophantine Approximations written by Umberto Zannier and published by Springer. This book was released on 2015-02-13 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diophantine Approximation and Its Applications by : Charles F. Osgood
Download or read book Diophantine Approximation and Its Applications written by Charles F. Osgood and published by . This book was released on 1973 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Book Synopsis Some applications of Diophantine Approximation to Diophantine Equations. With Special Emphasis on the Schmidt Subspace Theorem by : Umberto Zannier
Download or read book Some applications of Diophantine Approximation to Diophantine Equations. With Special Emphasis on the Schmidt Subspace Theorem written by Umberto Zannier and published by . This book was released on 2003 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Some Applications of Diophantine Approximations by : Carl Ludwig Siegel
Download or read book On Some Applications of Diophantine Approximations written by Carl Ludwig Siegel and published by . This book was released on 2014 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications of Diophantine Approximation to Integral Points and Transcendence by : Pietro Corvaja
Download or read book Applications of Diophantine Approximation to Integral Points and Transcendence written by Pietro Corvaja and published by Cambridge University Press. This book was released on 2018-05-03 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.
Book Synopsis On Some Applications of Diophantine Approximations a translation of Carl Ludwig Siegel's Über einige Anwendungen diophantischer Approximationen by Clemens Fuchs, with a commentary and the article Integral points on curves by : C. L. Siegel
Download or read book On Some Applications of Diophantine Approximations a translation of Carl Ludwig Siegel's Über einige Anwendungen diophantischer Approximationen by Clemens Fuchs, with a commentary and the article Integral points on curves written by C. L. Siegel and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diophantine Approximations by : Ivan Niven
Download or read book Diophantine Approximations written by Ivan Niven and published by Courier Corporation. This book was released on 2013-01-23 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 1995-06-29 with total page 146 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.
Book Synopsis An Introduction to Diophantine Approximation by : John William Scott Cassels
Download or read book An Introduction to Diophantine Approximation written by John William Scott Cassels and published by . This book was released on 1972 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diophantine Approximation on Linear Algebraic Groups by : Michel Waldschmidt
Download or read book Diophantine Approximation on Linear Algebraic Groups written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Some Applications of Diophantine Approximation by : R. Tijdeman
Download or read book Some Applications of Diophantine Approximation written by R. Tijdeman and published by . This book was released on 2000 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diophantine Approximation by : David Masser
Download or read book Diophantine Approximation written by David Masser and published by Springer. This book was released on 2008-02-01 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diophantine Approximation and Abelian Varieties by : Bas Edixhoven
Download or read book Diophantine Approximation and Abelian Varieties written by Bas Edixhoven and published by Springer. This book was released on 2009-02-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper "Diophantine approximation on abelian varieties", Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.
Book Synopsis Diophantine approximations by special points and applications to Dynamics and Geometry by : Vesselin Atanasov Dimitrov
Download or read book Diophantine approximations by special points and applications to Dynamics and Geometry written by Vesselin Atanasov Dimitrov and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diophantine Analysis by : Jorn Steuding
Download or read book Diophantine Analysis written by Jorn Steuding and published by CRC Press. This book was released on 2005-05-19 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diophantine Approximation by : Robert F. Tichy
Download or read book Diophantine Approximation written by Robert F. Tichy and published by Springer Science & Business Media. This book was released on 2008-07-10 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
