[PDF] Unit Equations In Diophantine Number Theory eBook

Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 381 pages
File Size : 37,15 MB
Release : 2015-12-30
Category : Mathematics
ISBN : 1316432351

GET BOOK

Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 477 pages
File Size : 32,56 MB
Release : 2017
Category : Mathematics
ISBN : 1107097614

GET BOOK

The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 26,73 MB
Release : 2007-05-23
Category : Mathematics
ISBN : 0387499229

GET BOOK

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.

Author : Wolfgang M. Schmidt
Publisher : Springer
Page : 224 pages
File Size : 43,93 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540473742

GET BOOK

"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 : István Gaál
Publisher : Springer Nature
Page : 326 pages
File Size : 35,85 MB
Release : 2019-09-03
Category : Mathematics
ISBN : 3030238652

GET BOOK

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.

Author : Istvan Gaal
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 37,38 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461200857

GET BOOK

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.

Author : Open University M381/Number theory/Unit 8
Publisher :
Page : 48 pages
File Size : 35,71 MB
Release : 2009-05-16
Category : Diophantine equations
ISBN : 9780749222789

GET BOOK

Topics covered in this unit include Pell's equation, The Pythagorean equation, Fermat's last Theorem, and Sums of squares.To order all 8 units in the Number Theory series please see produc M381/PP02

Author : Róbert Freud
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 48,53 MB
Release : 2020-10-08
Category : Education
ISBN : 1470452758

GET BOOK

Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.

Author : Umberto Zannier
Publisher : Springer
Page : 248 pages
File Size : 11,27 MB
Release : 2015-05-05
Category : Mathematics
ISBN : 8876425179

GET BOOK

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.