Lecture Notes on Diophantine Analysis

Lecture Notes on Diophantine Analysis
Author :
Publisher : Springer
Total Pages : 248
Release :
ISBN-10 : 9788876425172
ISBN-13 : 8876425179
Rating : 4/5 (72 Downloads)

Synopsis Lecture Notes on Diophantine Analysis by : Umberto Zannier

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 Analysis

Diophantine Analysis
Author :
Publisher : Birkhäuser
Total Pages : 239
Release :
ISBN-10 : 9783319488172
ISBN-13 : 3319488171
Rating : 4/5 (72 Downloads)

Synopsis Diophantine Analysis by : Jörn Steuding

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.

Diophantine Approximations and Diophantine Equations

Diophantine Approximations and Diophantine Equations
Author :
Publisher : Springer
Total Pages : 224
Release :
ISBN-10 : 9783540473749
ISBN-13 : 3540473742
Rating : 4/5 (49 Downloads)

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

"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 Over Function Fields

Diophantine Equations Over Function Fields
Author :
Publisher : Cambridge University Press
Total Pages : 142
Release :
ISBN-10 : 0521269830
ISBN-13 : 9780521269834
Rating : 4/5 (30 Downloads)

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

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

An Introduction to Diophantine Equations

An Introduction to Diophantine Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 350
Release :
ISBN-10 : 9780817645496
ISBN-13 : 0817645497
Rating : 4/5 (96 Downloads)

Synopsis An Introduction to Diophantine Equations by : Titu Andreescu

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.

Classical Diophantine Equations

Classical Diophantine Equations
Author :
Publisher : Springer
Total Pages : 244
Release :
ISBN-10 : 9783540480839
ISBN-13 : 3540480838
Rating : 4/5 (39 Downloads)

Synopsis Classical Diophantine Equations by : Vladimir G. Sprindzuk

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.

Exploring the Number Jungle: A Journey into Diophantine Analysis

Exploring the Number Jungle: A Journey into Diophantine Analysis
Author :
Publisher : American Mathematical Soc.
Total Pages : 160
Release :
ISBN-10 : 9780821826409
ISBN-13 : 0821826409
Rating : 4/5 (09 Downloads)

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

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.

Integral Points on Algebraic Varieties

Integral Points on Algebraic Varieties
Author :
Publisher : Springer
Total Pages : 82
Release :
ISBN-10 : 9789811026485
ISBN-13 : 9811026483
Rating : 4/5 (85 Downloads)

Synopsis Integral Points on Algebraic Varieties by : Pietro Corvaja

This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.

Algebraic Number Theory and Diophantine Analysis

Algebraic Number Theory and Diophantine Analysis
Author :
Publisher : Walter de Gruyter
Total Pages : 576
Release :
ISBN-10 : 3110163047
ISBN-13 : 9783110163049
Rating : 4/5 (47 Downloads)

Synopsis Algebraic Number Theory and Diophantine Analysis by : Franz Halter-Koch

No detailed description available for "Algebraic Number Theory and Diophantine Analysis".