Analytic Methods For Diophantine Equations And Diophantine Inequalities

Author : H. Davenport
Publisher : Cambridge University Press
ISBN 13 : 9781139441230
Total Pages : 164 pages
Book Rating : 4.3X/5 ( download)

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Download or read book Analytic Methods for Diophantine Equations and Diophantine Inequalities written by H. Davenport and published by Cambridge University Press. This book was released on 2005-02-07 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : 0 pages
Book Rating : 4.63/5 ( download)

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Download or read book Analytic Methods for Diophantine Equations and Diophantine Inequalities written by Harold Davenport and published by . This book was released on 1962 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Harold Davenport
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.17/5 ( download)

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Download or read book Analytic Methods for Diophantine Equations written by Harold Davenport and published by . This book was released on 1962 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Yuan Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3642581714
Total Pages : 185 pages
Book Rating : 4.17/5 ( download)

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Download or read book Diophantine Equations and Inequalities in Algebraic Number Fields written by Yuan Wang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Marius Overholt
Publisher : American Mathematical Soc.
ISBN 13 : 1470417065
Total Pages : 394 pages
Book Rating : 4.62/5 ( download)

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Download or read book A Course in Analytic Number Theory written by Marius Overholt and published by American Mathematical Soc.. This book was released on 2014-12-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

Author : Roger Clive Baker
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.67/5 ( download)

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Download or read book Diophantine Inequalities written by Roger Clive Baker and published by Oxford University Press, USA. This book was released on 1986 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1107097606
Total Pages : 381 pages
Book Rating : 4.05/5 ( download)

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Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, graduate-level treatment of unit equations and their various applications.

Author : N.B. Singh
Publisher : N.B. Singh
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4./5 ( download)

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Download or read book Diophantine Discoveries written by N.B. Singh and published by N.B. Singh. This book was released on with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Diophantine Discoveries" is a captivating exploration of the world of Diophantine equations, showcasing the beauty and intellectual allure of these mathematical puzzles. Written with clarity and enthusiasm, the book guides readers through the historical and contemporary significance of Diophantine equations, illuminating the ingenious methods and solutions developed by mathematicians over the centuries. From Fermat's Last Theorem to modern applications, the book provides a concise and engaging journey into the realm of Diophantine equations, making the subject accessible to both mathematicians and curious minds alik

Author :
Publisher : Cambridge University Press
ISBN 13 : 0521573475
Total Pages : 248 pages
Book Rating : 4.74/5 ( download)

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Download or read book The Hardy-Littlewood Method written by and published by Cambridge University Press. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nihon Sūgakkai
Publisher : MIT Press
ISBN 13 : 9780262590204
Total Pages : 1180 pages
Book Rating : 4.04/5 ( download)

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Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.