Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 381 pages
File Size : 35,2 MB
Release : 2015-12-30
Category : Mathematics
ISBN : 1107097606
A comprehensive, graduate-level treatment of unit equations and their various applications.
Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 381 pages
File Size : 32,46 MB
Release : 2015-12-30
Category : Mathematics
ISBN : 1316432351
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 : 48,84 MB
Release : 2017
Category : Mathematics
ISBN : 1107097614
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 : 49,52 MB
Release : 2008-10-10
Category : Mathematics
ISBN : 0387499237
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 : Henri Cohen
Publisher : Springer Science & Business Media
Page : 619 pages
File Size : 27,43 MB
Release : 2008-12-17
Category : Mathematics
ISBN : 038749894X
This book deals with several aspects of what is now called "explicit number theory." The central theme 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 local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
Author : Wolfgang M. Schmidt
Publisher : Springer
Page : 224 pages
File Size : 36,72 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540473742
"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 : Jennifer S. Balakrishnan
Publisher : Springer Nature
Page : 587 pages
File Size : 40,34 MB
Release : 2022-03-15
Category : Mathematics
ISBN : 3030809145
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 241 pages
File Size : 36,32 MB
Release : 2022-04-28
Category : Mathematics
ISBN : 1009005855
Provides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.
Author : Rafael von Känel
Publisher : American Mathematical Society
Page : 154 pages
File Size : 18,44 MB
Release : 2023-06-22
Category : Mathematics
ISBN : 1470464160
View the abstract.
Author : Kağan Kurşungöz
Publisher : Walter de Gruyter GmbH & Co KG
Page : 112 pages
File Size : 14,52 MB
Release : 2021-11-08
Category : Mathematics
ISBN : 3110761114
Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory. Original research is presented that discusses modern techniques and survey papers from selected academic scholars.
