[PDF] Lecture Notes On Diophantine Analysis eBook

Author : Umberto Zannier
Publisher : Springer
Page : 248 pages
File Size : 24,11 MB
Release : 2015-05-05
Category : Mathematics
ISBN : 8876425179

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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.

Author : Jörn Steuding
Publisher : Birkhäuser
Page : 239 pages
File Size : 29,76 MB
Release : 2016-12-21
Category : Mathematics
ISBN : 3319488171

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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.

Author : Wolfgang M. Schmidt
Publisher : Springer
Page : 224 pages
File Size : 36,78 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540473742

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"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

Author : Australian Mathematical Society. Convention
Publisher : Cambridge University Press
Page : 184 pages
File Size : 25,35 MB
Release : 1986-07-17
Category : Mathematics
ISBN : 9780521339230

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These papers were presented at the 1985 Australian Mathematical Society convention. They survey recent work in Diophantine analysis.

Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 19,52 MB
Release : 2010-09-02
Category : Mathematics
ISBN : 0817645497

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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.

Author : Australian Mathematical Society
Publisher :
Page : 182 pages
File Size : 16,22 MB
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 9781107087835

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These papers were presented at the 1985 Australian Mathematical Society convention. They survey recent work in Diophantine analysis.

Author : R. C. Mason
Publisher : Cambridge University Press
Page : 142 pages
File Size : 49,71 MB
Release : 1984-04-26
Category : Mathematics
ISBN : 9780521269834

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A self-contained account of a new approach to the subject.

Author : Edward B. Burger
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 15,35 MB
Release : 2000
Category : Mathematics
ISBN : 0821826409

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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.