**Author**: M. Ram Murty,Jody (Indigo) Esmonde

**Publisher:**Springer Science & Business Media

**ISBN:**0387269983

**Category:**Mathematics

**Page:**352

**View:**3668

Skip to content
# Search Results for: problems-in-algebraic-number-theory-graduate-texts-in-mathematics

**Author**: M. Ram Murty,Jody (Indigo) Esmonde

**Publisher:** Springer Science & Business Media

**ISBN:** 0387269983

**Category:** Mathematics

**Page:** 352

**View:** 3668

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**: Maruti Ram Murty

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387951430

**Category:** Mathematics

**Page:** 452

**View:** 8124

This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate and senior undergraduate students. The goal is to give a rapid introduction of how analytic methods are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory.

**Author**: Erich Hecke

**Publisher:** University of Pennsylvania Press

**ISBN:** 9780821821435

**Category:** Mathematics

**Page:** 274

**View:** 1421

This title has been described as An elegant and comprehensive account of the modern theory of algebraic numbers - Bulletin of the AMS.

**Author**: Henri Cohen

**Publisher:** Springer Science & Business Media

**ISBN:** 3662029456

**Category:** Mathematics

**Page:** 536

**View:** 1197

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.

**Author**: Robert B. Ash

**Publisher:** Courier Corporation

**ISBN:** 0486477541

**Category:** Mathematics

**Page:** 112

**View:** 3520

This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.
*Right Triangles, Sums of Squares, and Arithmetic*

**Author**: Ramin Takloo-Bighash

**Publisher:** Springer

**ISBN:** 3030026043

**Category:** Mathematics

**Page:** 279

**View:** 453

Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.
*A Genetic Introduction to Algebraic Number Theory*

**Author**: Harold M. Edwards

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387950020

**Category:** Mathematics

**Page:** 407

**View:** 6502

This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.

**Author**: A. Fröhlich,M. J. Taylor,Martin J. Taylor

**Publisher:** Cambridge University Press

**ISBN:** 9780521438346

**Category:** Mathematics

**Page:** 355

**View:** 2208

This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, combining at each stage theory with explicit computations.

**Author**: H. Koch,Helmut Koch

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540630036

**Category:** Mathematics

**Page:** 269

**View:** 701

This book is an exposition of the main ideas of algebraic number theory. It is written for the non-expert. Therefore, beyond some algebra, there are almost no prerequisites.

**Author**: Komaravolu Chandrasekharan

**Publisher:** Springer-Verlag

**ISBN:** 3540348557

**Category:** Mathematics

**Page:** 203

**View:** 8665

**Author**: Melvyn B. Nathanson,Springer-Verlag

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387989129

**Category:** Mathematics

**Page:** 513

**View:** 2159

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.

**Author**: E. T. Hecke

**Publisher:** Springer Science & Business Media

**ISBN:** 1475740921

**Category:** Mathematics

**Page:** 242

**View:** 8520

. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.

**Author**: Melvyn B. Nathanson

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387946566

**Category:** Mathematics

**Page:** 342

**View:** 7365

[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.

**Author**: N.A

**Publisher:** Academic Press

**ISBN:** 9780080873329

**Category:** Mathematics

**Page:** 434

**View:** 4133

This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

**Author**: Jean Pierre Serre

**Publisher:** Springer-Verlag

**ISBN:** 3322858634

**Category:** Mathematics

**Page:** 102

**View:** 7965

**Author**: Kenneth Ireland,Michael Rosen

**Publisher:** Springer Science & Business Media

**ISBN:** 147572103X

**Category:** Mathematics

**Page:** 394

**View:** 5391

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

**Author**: John Stillwell

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387955872

**Category:** Mathematics

**Page:** 256

**View:** 1843

Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

**Author**: Marius Overholt

**Publisher:** American Mathematical Soc.

**ISBN:** 1470417065

**Category:** Mathematics

**Page:** 371

**View:** 5154

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.
*Glanzlichter der Zahlentheorie*

**Author**: Paulo Ribenboim

**Publisher:** Springer-Verlag

**ISBN:** 3540879579

**Category:** Mathematics

**Page:** 391

**View:** 2638

Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.

**Author**: Melvyn B. Nathanson

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387946559

**Category:** Mathematics

**Page:** 296

**View:** 4060

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.

Full PDF Download Free

Privacy Policy

Copyright © 2019 Download PDF Site — Primer WordPress theme by GoDaddy