Discriminant Equations in Diophantine Number Theory PDF Download
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Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097614
Category : Mathematics
Languages : en
Pages : 477
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Book Description
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097614
Category : Mathematics
Languages : en
Pages : 477
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Book Description
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author: J. H. Evertse
Publisher:
ISBN: 9781316729014
Category : MATHEMATICS
Languages : en
Pages :
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Book Description
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1316432351
Category : Mathematics
Languages : en
Pages : 381
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Book Description
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: Daniel E. Flath
Publisher: American Mathematical Soc.
ISBN: 1470446944
Category : Number theory
Languages : en
Pages : 212
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Book Description
Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p−q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled Δ=b2−4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.
Author: Henri Cohen
Publisher: Springer Science & Business Media
ISBN: 0387499229
Category : Mathematics
Languages : en
Pages : 673
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Book Description
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: Daniel Duverney
Publisher: World Scientific
ISBN: 9814307459
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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. These topics are covered in 12 chapters and more than 200 solved exercises. Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.
Author: Michael Jacobson
Publisher: Springer Science & Business Media
ISBN: 0387849238
Category : Mathematics
Languages : en
Pages : 495
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Book Description
Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.
Author: Vladimir G. Sprindzuk
Publisher: Springer
ISBN: 3540480838
Category : Mathematics
Languages : en
Pages : 244
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Book Description
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.
Author: Leonard Eugene Dickson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Author: Leonard Eugene Dickson
Publisher: Courier Corporation
ISBN: 0486442349
Category : Mathematics
Languages : en
Pages : 325
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Book Description
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This final volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to quadratic and higher forms. It can be read independently of the preceding volumes, which explore divisibility and primality and diophantine analysis. Topics include reduction and equivalence of binary quadratic forms and representation of integers; composition of binary quadratic forms; the composition of orders and genera; irregular determinants; classes of binary quadratic forms with integral coefficients; binary quadratic forms whose coefficients are complete integers or integers of a field; classes of binary quadratic forms with complex integral coefficients; ternary and quaternary quadratic forms; cubic forms in three or more variables; binary hermitian forms; bilinear forms, matrices, and linear substitutions; congruencial theory of forms; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
