The Hardy Littlewood Method

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The Hardy-Littlewood Method

Author : R. C. Vaughan
Publisher : Cambridge University Press
ISBN 13 : 9780521234399
Total Pages : 184 pages
Book Rating : 4.2/5 (343 download)

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Book Synopsis The Hardy-Littlewood Method by : R. C. Vaughan

Download or read book The Hardy-Littlewood Method written by R. C. Vaughan and published by Cambridge University Press. This book was released on 1981-07-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hardy-Littlewood method is a means of estimating the number of integer solutions of equations and was first applied to Waring's problem on representations of integers by sums of powers. This introduction to the method deals with its classical forms and outlines some of the more recent developments. Now in its second edition it has been fully updated; the author has made extensive revisions and added a new chapter to take account of major advances by Vaughan and Wooley. The reader is expected to be familiar with elementary number theory and postgraduate students should find it of great use as an advanced textbook. It will also be indispensable to all lecturers and research workers interested in number theory.

The Hardy-Littlewood Method

Author :
Publisher : Cambridge University Press
ISBN 13 : 0521573475
Total Pages : 248 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis The Hardy-Littlewood Method by :

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:

Cubic Forms and the Circle Method

Author : Tim Browning
Publisher : Springer Nature
ISBN 13 : 3030868729
Total Pages : 175 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Cubic Forms and the Circle Method by : Tim Browning

Download or read book Cubic Forms and the Circle Method written by Tim Browning and published by Springer Nature. This book was released on 2021-11-19 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Quantitative Arithmetic of Projective Varieties

Author : Timothy D. Browning
Publisher : Springer Science & Business Media
ISBN 13 : 3034601298
Total Pages : 160 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Quantitative Arithmetic of Projective Varieties by : Timothy D. Browning

Download or read book Quantitative Arithmetic of Projective Varieties written by Timothy D. Browning and published by Springer Science & Business Media. This book was released on 2009-12-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties.

Inequalities

Author : G. H. Hardy
Publisher : Cambridge University Press
ISBN 13 : 9780521358804
Total Pages : 344 pages
Book Rating : 4.3/5 (588 download)

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Book Synopsis Inequalities by : G. H. Hardy

Download or read book Inequalities written by G. H. Hardy and published by Cambridge University Press. This book was released on 1952 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Real-Variable Methods in Harmonic Analysis

Author : Alberto Torchinsky
Publisher : Elsevier
ISBN 13 : 1483268888
Total Pages : 474 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Real-Variable Methods in Harmonic Analysis by : Alberto Torchinsky

Download or read book Real-Variable Methods in Harmonic Analysis written by Alberto Torchinsky and published by Elsevier. This book was released on 2016-06-03 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.

The Method of Trigonometrical Sums in the Theory of Numbers

Author : I. M. Vinogradov
Publisher : Courier Corporation
ISBN 13 : 0486154521
Total Pages : 194 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Method of Trigonometrical Sums in the Theory of Numbers by : I. M. Vinogradov

Download or read book The Method of Trigonometrical Sums in the Theory of Numbers written by I. M. Vinogradov and published by Courier Corporation. This book was released on 2013-10-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.

Analytic Methods for Diophantine Equations and Diophantine Inequalities

Author : H. Davenport
Publisher : Cambridge University Press
ISBN 13 : 9781139441230
Total Pages : 164 pages
Book Rating : 4.4/5 (412 download)

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Book Synopsis Analytic Methods for Diophantine Equations and Diophantine Inequalities by : H. Davenport

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.

Rational Number Theory in the 20th Century

Author : Władysław Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 0857295322
Total Pages : 659 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Rational Number Theory in the 20th Century by : Władysław Narkiewicz

Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.

The G. H. Hardy Reader

Author : Donald J. Albers
Publisher : Cambridge University Press
ISBN 13 : 1107135559
Total Pages : 413 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis The G. H. Hardy Reader by : Donald J. Albers

Download or read book The G. H. Hardy Reader written by Donald J. Albers and published by Cambridge University Press. This book was released on 2016-04-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: G. H. Hardy ranks among the greatest twentieth-century mathematicians. This book introduces this extraordinary individual and his writing.

Hardy-Littlewood and Ulyanov Inequalities

Author : Yurii Kolomoitsev
Publisher : American Mathematical Society
ISBN 13 : 1470447584
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hardy-Littlewood and Ulyanov Inequalities by : Yurii Kolomoitsev

Download or read book Hardy-Littlewood and Ulyanov Inequalities written by Yurii Kolomoitsev and published by American Mathematical Society. This book was released on 2021-09-24 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Real Analysis: A Comprehensive Course in Analysis, Part 1

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470410990
Total Pages : 789 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Real Analysis: A Comprehensive Course in Analysis, Part 1 by : Barry Simon

Download or read book Real Analysis: A Comprehensive Course in Analysis, Part 1 written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Additive Number Theory The Classical Bases

Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
ISBN 13 : 1475738455
Total Pages : 350 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Additive Number Theory The Classical Bases by : Melvyn B. Nathanson

Download or read book Additive Number Theory The Classical Bases written by Melvyn B. Nathanson and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

An Introduction to Measure Theory

Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Measure Theory by : Terence Tao

Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Ramanujan's Place in the World of Mathematics

Author : Krishnaswami Alladi
Publisher : Springer Science & Business Media
ISBN 13 : 813220767X
Total Pages : 179 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Ramanujan's Place in the World of Mathematics by : Krishnaswami Alladi

Download or read book Ramanujan's Place in the World of Mathematics written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians throughout the history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life and of the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. In the book, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his pathbreaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being.

数论导引

Author :
Publisher :
ISBN 13 : 9787115156112
Total Pages : 435 pages
Book Rating : 4.1/5 (561 download)

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Book Synopsis 数论导引 by :

Download or read book 数论导引 written by and published by . This book was released on 2007 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。

Number Theory for Computing

Author : Song Y. Yan
Publisher : Springer Science & Business Media
ISBN 13 : 366204773X
Total Pages : 454 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Number Theory for Computing by : Song Y. Yan

Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.