Unit Equations in Diophantine Number Theory

Nonfiction, Science & Nature, Mathematics, Number Theory
Cover of the book Unit Equations in Diophantine Number Theory by Jan-Hendrik Evertse, Kálmán Győry, Cambridge University Press
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Author: Jan-Hendrik Evertse, Kálmán Győry ISBN: 9781316430224
Publisher: Cambridge University Press Publication: December 30, 2015
Imprint: Cambridge University Press Language: English
Author: Jan-Hendrik Evertse, Kálmán Győry
ISBN: 9781316430224
Publisher: Cambridge University Press
Publication: December 30, 2015
Imprint: Cambridge University Press
Language: English

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.

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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.

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