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Author : Jan-Hendrik Evertse,Kálmán Győry
Publisher : Unknown
Page : 128 pages
File Size : 40,8 Mb
Release : 2016
Category : Electronic
ISBN : 1316160769
Author : J. H. Evertse,Kálmán Györy
Publisher : Unknown
Page : 128 pages
File Size : 44,9 Mb
Release : 2016
Category : MATHEMATICS
ISBN : 131672901X
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author : Jan-Hendrik Evertse,Klmn Gyory
Publisher : Cambridge University Press
Page : 477 pages
File Size : 51,8 Mb
Release : 2016-11-03
Category : Mathematics
ISBN : 9781107097612
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author : Jan-Hendrik Evertse,Klmn Gyory
Publisher : Cambridge University Press
Page : 381 pages
File Size : 49,7 Mb
Release : 2015-12-30
Category : Mathematics
ISBN : 9781107097605
A comprehensive, graduate-level treatment of unit equations and their various applications.
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 47,5 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9780387499222
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 E. Flath
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 55,5 Mb
Release : 2018-09-27
Category : Number theory
ISBN : 9781470446949
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 : Daniel Duverney
Publisher : World Scientific
Page : 348 pages
File Size : 50,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814307451
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,Hugh Williams
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 51,8 Mb
Release : 2008-12-04
Category : Mathematics
ISBN : 9780387849232
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
Page : 244 pages
File Size : 46,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540480839
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,G. H. Cresse
Publisher : Courier Corporation
Page : 325 pages
File Size : 48,8 Mb
Release : 2005-06-03
Category : Mathematics
ISBN : 9780486442341
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.
Author : Christian Elsholtz,Peter Grabner
Publisher : Springer
Page : 444 pages
File Size : 42,5 Mb
Release : 2017-05-26
Category : Mathematics
ISBN : 9783319553573
This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy’s research interests and which he significantly shaped, including Diophantine problems, asymptotic counting, uniform distribution and discrepancy of sequences (in theory and application), dynamical systems, prime numbers, and actuarial mathematics. Offering valuable insights into recent developments in these areas, the book will be of interest to researchers and graduate students engaged in number theory and its applications.
Author : István Gaál
Publisher : Springer Nature
Page : 326 pages
File Size : 41,8 Mb
Release : 2019-09-03
Category : Mathematics
ISBN : 9783030238650
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.
Author : Kalman Gyoery,Attila Pethoe,Vera T. Sos
Publisher : Walter de Gruyter
Page : 617 pages
File Size : 55,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110809794
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.
Author : Richard Mollin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 676 pages
File Size : 43,6 Mb
Release : 2016-12-19
Category : Mathematics
ISBN : 9783110848632
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.
Author : Istvan Gaal
Publisher : Springer Science & Business Media
Page : 76 pages
File Size : 48,9 Mb
Release : 2002-04-26
Category : Mathematics
ISBN : 0817642714
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.
