Multiplicative Number Theory

Author : H. Davenport
Publisher : Springer Science & Business Media
Page : 188 pages
File Size : 54,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475759273

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Multiplicative Number Theory by H. Davenport Pdf

Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimula tion, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate tor L timctions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted.

Author : Hugh L. Montgomery,Robert C. Vaughan
Publisher : Cambridge University Press
Page : 574 pages
File Size : 51,7 Mb
Release : 2007
Category : Mathematics
ISBN : 0521849039

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Multiplicative Number Theory I by Hugh L. Montgomery,Robert C. Vaughan Pdf

A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.

Author : Hugh L. Montgomery
Publisher : Springer
Page : 187 pages
File Size : 42,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540369356

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Topics in Multiplicative Number Theory by Hugh L. Montgomery Pdf

Author : Bowen Kerins, Darryl Yong,Al Cuoco,Glenn Stevens
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 55,7 Mb
Release : 2015-10-15
Category : Education
ISBN : 9781470421953

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Famous Functions in Number Theory by Bowen Kerins, Darryl Yong,Al Cuoco,Glenn Stevens Pdf

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : Tom M. Apostol
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 54,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475755794

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Introduction to Analytic Number Theory by Tom M. Apostol Pdf

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS

Author : Tianxin Cai
Publisher : World Scientific
Page : 430 pages
File Size : 45,7 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9789811218316

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A Modern Introduction To Classical Number Theory by Tianxin Cai Pdf

Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him a full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.One feature of the book is the supplementary material after each section, there by broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler's conjecture, Fermat's Last Theorem, Laudau's problem and etc.This book is written for anyone who loves natural numbers, and it can also be read by mathematics majors, graduate students, and researchers. The book contains many illustrations and tables. Readers can appreciate the author's sensitivity of history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.

Author : G. Tenenbaum
Publisher : Cambridge University Press
Page : 180 pages
File Size : 43,8 Mb
Release : 1995-06-30
Category : Mathematics
ISBN : 0521412617

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Introduction to Analytic and Probabilistic Number Theory by G. Tenenbaum Pdf

This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 46,9 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 47,9 Mb
Release : 2008-01-11
Category : Mathematics
ISBN : 9780387227382

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Elementary Methods in Number Theory by Melvyn B. Nathanson Pdf

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.

Author : John B. Friedlander,Henryk Iwaniec
Publisher : American Mathematical Soc.
Page : 554 pages
File Size : 45,6 Mb
Release : 2010-06-22
Category : Mathematics
ISBN : 9780821849705

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Opera de Cribro by John B. Friedlander,Henryk Iwaniec Pdf

This is a true masterpiece that will prove to be indispensable to the serious researcher for many years to come. --Enrico Bombieri, Institute for Advanced Study This is a truly comprehensive account of sieves and their applications, by two of the world's greatest authorities. Beginners will find a thorough introduction to the subject, with plenty of helpful motivation. The more practised reader will appreciate the authors' insights into some of the more mysterious parts of the theory, as well as the wealth of new examples. --Roger Heath-Brown, University of Oxford, Fellow of Royal Society This is a comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. Included is a wide range of applications, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. New proofs are given also of some of the central theorems of analytic number theory; these proofs emphasize and take advantage of the applicability of sieve ideas. The book contains numerous comments which provide the reader with insight into the workings of the subject, both as to what the sieve can do and what it cannot do. The authors reveal recent developements by which the parity barrier can be breached, exposing golden nuggets of the subject, previously inaccessible. The variety in the topics covered and in the levels of difficulty encountered makes this a work of value to novices and experts alike, both as an educational tool and a basic reference.

Author : M. Ram Murty,Jody (Indigo) Esmonde
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 40,7 Mb
Release : 2005-09-28
Category : Mathematics
ISBN : 9780387269986

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Problems in Algebraic Number Theory by M. Ram Murty,Jody (Indigo) Esmonde Pdf

The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

Author : Tom M. Apostol
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209997

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Modular Functions and Dirichlet Series in Number Theory by Tom M. Apostol Pdf

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.

Author : Martin Lorenz
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 45,7 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 9783540273585

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Multiplicative Invariant Theory by Martin Lorenz Pdf

Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.

Author : H. E. Rose
Publisher : Oxford University Press
Page : 420 pages
File Size : 41,8 Mb
Release : 1995
Category : Mathematics
ISBN : 0198523769

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A Course in Number Theory by H. E. Rose Pdf

This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.

Author : Wissam Raji
Publisher : The Saylor Foundation
Page : 171 pages
File Size : 48,8 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 8210379456XXX

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An Introductory Course in Elementary Number Theory by Wissam Raji Pdf

These notes serve as course notes for an undergraduate course in number theory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required. The exercises are carefully chosen to broaden the understanding of the concepts. Moreover, these notes shed light on analytic number theory, a subject that is rarely seen or approached by undergraduate students. One of the unique characteristics of these notes is the careful choice of topics and its importance in the theory of numbers. The freedom is given in the last two chapters because of the advanced nature of the topics that are presented.