Analytic Methods for Diophantine Equations and Diophantine Inequalities PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Analytic Methods for Diophantine Equations and Diophantine Inequalities PDF full book. Access full book title Analytic Methods for Diophantine Equations and Diophantine Inequalities by H. Davenport. Download full books in PDF and EPUB format.
Author: H. Davenport
Publisher: Cambridge University Press
ISBN: 9781139441230
Category : Mathematics
Languages : en
Pages : 164
Get Book Here
Book Description
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: H. Davenport
Publisher: Cambridge University Press
ISBN: 9781139441230
Category : Mathematics
Languages : en
Pages : 164
Get Book Here
Book Description
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:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Harold Davenport
Publisher:
ISBN:
Category :
Languages : en
Pages : 168
Get Book Here
Book Description
Author: Yuan Wang
Publisher: Springer Science & Business Media
ISBN: 3642581714
Category : Mathematics
Languages : en
Pages : 185
Get Book Here
Book Description
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: Jorn Steuding
Publisher: CRC Press
ISBN: 1584884827
Category : Mathematics
Languages : en
Pages : 275
Get Book Here
Book Description
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:
Publisher: American Mathematical Soc.
ISBN: 9780821830901
Category : Mathematics
Languages : en
Pages : 340
Get Book Here
Book Description
This collection consists of papers delivered at an international conference by the most eminent specialists in the domains of number theory, algebra, and analysis. The papers are devoted to actual problems in these domains of mathematics. In addition, short communications presented by participants in the conference are included.
Author: R. C. Mason
Publisher: Cambridge University Press
ISBN: 9780521269834
Category : Mathematics
Languages : en
Pages : 142
Get Book Here
Book Description
A self-contained account of a new approach to the subject.
Author: Heinrich G. W. Begehr
Publisher: World Scientific
ISBN: 9789810215507
Category : Mathematics
Languages : en
Pages : 288
Get Book Here
Book Description
This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincar‚ problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.
Author: Titu Andreescu
Publisher: Springer
ISBN: 0387541098
Category : Mathematics
Languages : en
Pages : 224
Get Book Here
Book Description
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: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097606
Category : Mathematics
Languages : en
Pages : 381
Get Book Here
Book Description
A comprehensive, graduate-level treatment of unit equations and their various applications.
