Analytic Methods For Diophantine Equations And Diophantine Inequalities
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Author |
: H. Davenport |
Publisher |
: Cambridge University Press |
Total Pages |
: 164 |
Release |
: 2005-02-07 |
ISBN-10 |
: 113944123X |
ISBN-13 |
: 9781139441230 |
Rating |
: 4/5 (3X Downloads) |
Synopsis Analytic Methods for Diophantine Equations and Diophantine Inequalities by : H. Davenport
Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.
Author |
: Harold Davenport |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 1962 |
ISBN-10 |
: OCLC:918205863 |
ISBN-13 |
: |
Rating |
: 4/5 (63 Downloads) |
Synopsis Analytic Methods for Diophantine Equations and Diophantine Inequalities by : Harold Davenport
Author |
: Harold Davenport |
Publisher |
: |
Total Pages |
: 168 |
Release |
: 1962 |
ISBN-10 |
: OCLC:1057852317 |
ISBN-13 |
: |
Rating |
: 4/5 (17 Downloads) |
Synopsis Analytic Methods for Diophantine Equations by : Harold Davenport
Author |
: Jorn Steuding |
Publisher |
: CRC Press |
Total Pages |
: 275 |
Release |
: 2005-05-19 |
ISBN-10 |
: 9781584884828 |
ISBN-13 |
: 1584884827 |
Rating |
: 4/5 (28 Downloads) |
Synopsis Diophantine Analysis by : Jorn Steuding
While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers. Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.
Author |
: Titu Andreescu |
Publisher |
: Springer |
Total Pages |
: 224 |
Release |
: 2015-06-29 |
ISBN-10 |
: 9780387541099 |
ISBN-13 |
: 0387541098 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Quadratic Diophantine Equations by : Titu Andreescu
This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.
Author |
: Yuan Wang |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 185 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642581717 |
ISBN-13 |
: 3642581714 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Diophantine Equations and Inequalities in Algebraic Number Fields by : Yuan Wang
The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s(k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here
Author |
: R. C. Mason |
Publisher |
: Cambridge University Press |
Total Pages |
: 142 |
Release |
: 1984-04-26 |
ISBN-10 |
: 0521269830 |
ISBN-13 |
: 9780521269834 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Diophantine Equations Over Function Fields by : R. C. Mason
A self-contained account of a new approach to the subject.
Author |
: Titu Andreescu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 350 |
Release |
: 2010-09-02 |
ISBN-10 |
: 9780817645496 |
ISBN-13 |
: 0817645497 |
Rating |
: 4/5 (96 Downloads) |
Synopsis An Introduction to Diophantine Equations by : Titu Andreescu
This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Author |
: Roger Clive Baker |
Publisher |
: Oxford University Press, USA |
Total Pages |
: 298 |
Release |
: 1986 |
ISBN-10 |
: UOM:39015015607867 |
ISBN-13 |
: |
Rating |
: 4/5 (67 Downloads) |
Synopsis Diophantine Inequalities by : Roger Clive Baker
Starting with the work of I.M. Vinogradov and H. Heilbronn, the author develops the theme of nonlinear Diophantine approximation in a number of different directions.
Author |
: Jan-Hendrik Evertse |
Publisher |
: Cambridge University Press |
Total Pages |
: 381 |
Release |
: 2015-12-30 |
ISBN-10 |
: 9781107097605 |
ISBN-13 |
: 1107097606 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Unit Equations in Diophantine Number Theory by : Jan-Hendrik Evertse
A comprehensive, graduate-level treatment of unit equations and their various applications.