Number theory : an introduction via the density of primes / Benjamin Fine, Gerhard Rosenberger.
2016
QA241
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Details
Title
Number theory : an introduction via the density of primes / Benjamin Fine, Gerhard Rosenberger.
Edition
Second edition.
ISBN
9783319438757 (electronic book)
3319438751 (electronic book)
9783319438733
3319438751 (electronic book)
9783319438733
Published
Cham, Switzerland : Birkhäuser, 2016.
Language
English
Description
1 online resource (xiii, 413 pages) : illustrations.
Item Number
10.1007/978-3-319-43875-7 doi
Call Number
QA241
Dewey Decimal Classification
512.7
Summary
Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed October 7, 2016).
Added Author
Rosenberger, Gerhard, author.
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Table of Contents
Introduction and Historical Remarks
Basic Number Theory
The Infinitude of Primes
The Density of Primes
Primality Testing: An Overview
Primes and Algebraic Number Theory
The Fields Q_p of p-adic Numbers: Hensel's Lemma
References
Index.
Basic Number Theory
The Infinitude of Primes
The Density of Primes
Primality Testing: An Overview
Primes and Algebraic Number Theory
The Fields Q_p of p-adic Numbers: Hensel's Lemma
References
Index.