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Author : Harold Davenport
Publisher : Unknown
Page : 186 pages
File Size : 41,8 Mb
Release : 1962
Category : Diophantine analysis
ISBN : UOM:39015038956457
Author : H. Davenport
Publisher : Cambridge University Press
Page : 160 pages
File Size : 54,9 Mb
Release : 2005-02-07
Category : Mathematics
ISBN : 0521605830
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 : Yuan Wang
Publisher : Springer Science & Business Media
Page : 185 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581717
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.
Page : 394 pages
File Size : 51,8 Mb
Release : 2014-12-30
Category : Mathematics
ISBN : 9781470417062
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 : R. C. Mason
Publisher : Cambridge University Press
Page : 142 pages
File Size : 55,8 Mb
Release : 1984-04-26
Category : Mathematics
ISBN : 0521269830
A self-contained account of a new approach to the subject.
Author : Anonim
Publisher : Cambridge University Press
Page : 248 pages
File Size : 51,7 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9780521573474
Author : N.B. Singh
Publisher : N.B. Singh
Page : 66 pages
File Size : 45,7 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX
"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 : Roger Clive Baker
Publisher : Unknown
Page : 296 pages
File Size : 43,5 Mb
Release : 1986
Category : Diophantine analysis
ISBN : UCAL:B5008724
This book launches the prestigious new series London Mathematical Society Monographs. The author, noted for his work throughout the mathematical community, here presents an overview of the theory of nonlinear Diophantine approximation. He has concentrated on the important progress made in the last ten years by such contributors as I. M. Vinogradov, H. Heilbronn, and W. M. Schmidt, finding, for example, that it is possible to consider simultaneous approximation to integers by values of a set of quadratic forms, or a discrete analogue (small solutions of a system of homogeneous congruences).
Author : Nihon Sūgakkai
Publisher : MIT Press
Page : 1180 pages
File Size : 50,8 Mb
Release : 1993
Category : Mathematics
ISBN : 0262590204
V.1. A.N. v.2. O.Z. Apendices and indexes.
Author : Prapanpong Pongsriiam
Publisher : American Mathematical Society
Page : 402 pages
File Size : 51,9 Mb
Release : 2023-06-02
Category : Mathematics
ISBN : 9781470464448
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory. The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.
Author : Yuan Wang
Publisher : World Scientific
Page : 512 pages
File Size : 48,9 Mb
Release : 2005-06-07
Category : Mathematics
ISBN : 9789814480796
This volume presents a comprehensive collection of Wang Yuan's original important papers which are not available elsewhere, since the majority of the papers were published in China.Covering both pure number theory and applied mathematics, this book is important for understanding Wang Yuan's academic career and also the development of Chinese mathematics in recent years, since Wang Yuan's work has a wide-ranging influence in China.Wang Yuan is a professor and academician of the Chinese Academy of Sciences. He received his honorable Doctorship from Hong Kong Baptist University. He has published 70 papers and ten books.
Author : Henryk Iwaniec,Emmanuel Kowalski
Publisher : American Mathematical Soc.
Page : 615 pages
File Size : 41,5 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470467708
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Author : S. Lang
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 52,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662070109
It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.
Author : Hugh L. Montgomery,Robert C. Vaughan
Publisher : Cambridge University Press
Page : 574 pages
File Size : 53,6 Mb
Release : 2007
Category : Mathematics
ISBN : 0521849039
A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Author : Luis Dieulefait,Gerd Faltings,D. R. Heath-Brown
Publisher : Cambridge University Press
Page : 539 pages
File Size : 43,9 Mb
Release : 2015-10-08
Category : Mathematics
ISBN : 9781107462540
The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
