Algebraic Number Theory And Diophantine Analysis

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Algebraic Number Theory And Diophantine Analysis

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Author : Franz Halter-Koch
language : en
Publisher: Walter de Gruyter
Release Date : 2000

Algebraic Number Theory And Diophantine Analysis written by Franz Halter-Koch and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Number Theory

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Author : Henri Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-10

Number Theory written by Henri Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-10 with Mathematics categories.

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.

Number Theory

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Author : Daniel Duverney
language : en
Publisher: World Scientific
Release Date : 2010

Number Theory written by Daniel Duverney and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory. Clear, concise, and self-contained, the topics are covered in 12 chapters with more than 200 solved exercises. The textbook may be used by undergraduates and graduate students, as well as high school mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, the fascinating branch of mathematics.

Number Theory

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Author : Henri Cohen
language : en
Publisher: Springer
Release Date : 2007-05-23

Number Theory written by Henri Cohen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-23 with Mathematics categories.

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.

Algebraic Number Theory

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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Algebraic Number Theory written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which 1 make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collec tion of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of W eber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theo retically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, 1 have intermingled the ideal and idelic approaches without prejudice for either. 1 also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods).

Diophantine Equations And Power Integral Bases

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Author : István Gaál
language : en
Publisher: Springer Nature
Release Date : 2019-09-03

Diophantine Equations And Power Integral Bases written by István Gaál and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-03 with Mathematics categories.

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.

Discriminant Equations In Diophantine Number Theory

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Author : Jan-Hendrik Evertse
language : en
Publisher: Cambridge University Press
Release Date : 2017

Discriminant Equations In Diophantine Number Theory written by Jan-Hendrik Evertse and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.

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

Algebraic Geometry And Number Theory

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Author : Hussein Mourtada
language : en
Publisher: Birkhäuser
Release Date : 2017-05-07

Algebraic Geometry And Number Theory written by Hussein Mourtada and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-07 with Mathematics categories.

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Number Theory

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Author : Henri Cohen
language : en
Publisher: Springer
Release Date : 2008-11-01

Number Theory written by Henri Cohen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.

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.

Algebraic Number Theory And Fermat S Last Theorem

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Author : Ian Stewart
language : en
Publisher: CRC Press
Release Date : 2001-12-12

Algebraic Number Theory And Fermat S Last Theorem written by Ian Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-12 with Mathematics categories.

First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it