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Additive Number Theory The Classical Bases
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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.
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Download or read book 加{OCLCbr#E6}?{OCLCbr#A7}数{OCLCbr#E8}{OCLCbr#AE}? written by and published by . This book was released on 2012 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Number Theory and Additive Group Theory by : Alfred Geroldinger
Download or read book Combinatorial Number Theory and Additive Group Theory written by Alfred Geroldinger and published by Springer Science & Business Media. This book was released on 2009-04-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.
Book Synopsis Additive Number Theory by : David Chudnovsky
Download or read book Additive Number Theory written by David Chudnovsky and published by Springer Science & Business Media. This book was released on 2010-08-26 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.
Book Synopsis Elementary Methods in Number Theory by : Melvyn B. Nathanson
Download or read book Elementary Methods in Number Theory written by Melvyn B. Nathanson and published by Springer Science & Business Media. This book was released on 2008-01-11 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.
Book Synopsis Additive Theory of Prime Numbers by : Luogeng Hua
Download or read book Additive Theory of Prime Numbers written by Luogeng Hua and published by American Mathematical Soc.. This book was released on 2009-12-04 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Book Synopsis Combinatorial and Additive Number Theory IV by : Melvyn B. Nathanson
Download or read book Combinatorial and Additive Number Theory IV written by Melvyn B. Nathanson and published by Springer Nature. This book was released on 2021-08-12 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
Download or read book Additive Number Theory written by and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Melvyn B. Nathanson Publisher :Springer Science & Business Media ISBN 13 :9780387946559 Total Pages :320 pages Book Rating :4.9/5 (465 download)
Book Synopsis Additive Number Theory: Inverse Problems and the Geometry of Sumsets by : Melvyn B. Nathanson
Download or read book Additive Number Theory: Inverse Problems and the Geometry of Sumsets written by Melvyn B. Nathanson and published by Springer Science & Business Media. This book was released on 1996-08-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.
Book Synopsis Additive Number Theory of Polynomials Over a Finite Field by : Gove W. Effinger
Download or read book Additive Number Theory of Polynomials Over a Finite Field written by Gove W. Effinger and published by . This book was released on 1991 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps gather the sum of additive number theory.
Book Synopsis Combinatorial and Additive Number Theory by : Melvyn B. Nathanson
Download or read book Combinatorial and Additive Number Theory written by Melvyn B. Nathanson and published by Springer. This book was released on 2014-10-18 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.
Book Synopsis Combinatorial and Additive Number Theory II by : Melvyn B. Nathanson
Download or read book Combinatorial and Additive Number Theory II written by Melvyn B. Nathanson and published by Springer. This book was released on 2018-01-13 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling.
Book Synopsis Number Theory and Its Applications by : Cheon Seoung Ryoo
Download or read book Number Theory and Its Applications written by Cheon Seoung Ryoo and published by BoD – Books on Demand. This book was released on 2020-11-04 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on number theory and its applications has been done in mathematics, applied mathematics, and the sciences. In particular, number theory plays a fundamental and important role in mathematics and applied mathematics. This book is based on recent results in all areas related to number theory and its applications.
Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2007-05-23 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.
Book Synopsis A Course in Computational Algebraic Number Theory by : Henri Cohen
Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2000-08-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Book Synopsis Problems in Analytic Number Theory by : U.S.R. Murty
Download or read book Problems in Analytic Number Theory written by U.S.R. Murty and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In order to become proficient in mathematics, or in any subject," writes Andre Weil, "the student must realize that most topics in volve only a small number of basic ideas. " After learning these basic concepts and theorems, the student should "drill in routine exercises, by which the necessary reflexes in handling such concepts may be ac quired. . . . There can be no real understanding of the basic concepts of a mathematical theory without an ability to use them intelligently and apply them to specific problems. " Weil's insightfulobservation becomes especially important at the graduate and research level. It is the viewpoint of this book. Our goal is to acquaint the student with the methods of analytic number theory as rapidly as possible through examples and exercises. Any landmark theorem opens up a method of attacking other problems. Unless the student is able to sift out from the mass of theory the underlying techniques, his or her understanding will only be academic and not that of a participant in research. The prime number theorem has given rise to the rich Tauberian theory and a general method of Dirichlet series with which one can study the asymptotics of sequences. It has also motivated the development of sieve methods. We focus on this theme in the book. We also touch upon the emerging Selberg theory (in Chapter 8) and p-adic analytic number theory (in Chapter 10).
Book Synopsis Modular Functions and Dirichlet Series in Number Theory by : Tom M. Apostol
Download or read book Modular Functions and Dirichlet Series in Number Theory written by Tom M. Apostol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.
