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Unit Equations in Diophantine Number Theory

2015-12-30 Mathematics
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Release : 2015-12-30
Genre : Mathematics
Kind : eBook
Book Rating : 351/5 ( reviews)

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Book Synopsis Unit Equations in Diophantine Number Theory by : Jan-Hendrik Evertse

Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse. This book was released on 2015-12-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discriminant Equations in Diophantine Number Theory

2017 Mathematics
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Release : 2017
Genre : Mathematics
Kind : eBook
Book Rating : 614/5 ( reviews)

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Book Synopsis Discriminant Equations in Diophantine Number Theory by : Jan-Hendrik Evertse

Download or read book Discriminant Equations in Diophantine Number Theory written by Jan-Hendrik Evertse. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.

Number Theory

2007-05-23 Mathematics
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Release : 2007-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 229/5 ( reviews)

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Book Synopsis Number Theory by : Henri Cohen

Download or read book Number Theory written by Henri Cohen. This book was released on 2007-05-23. 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.

Diophantine Equations and Power Integral Bases

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 857/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

Diophantine Approximations and Diophantine Equations

2006-12-08 Mathematics
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Release : 2006-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 742/5 ( reviews)

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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. This book was released on 2006-12-08. 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

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