Number Theory

An Introduction via the Distribution of Primes

Authors: Fine, Benjamin, Rosenberger, Gerhard

  • Solid introduction to analytic number theory, including full proofs of Dirichlet’s Theorem and the Prime Number Theorem
  • Combines user-friendly style, historical context and a wide range of exercises from simple to complex, with selected solutions and tips
  • First treatment in book form of the AKS algorithm, showing that primality testing is of polynomial time
  • Offers interesting side topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers
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eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-4541-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this Textbook

This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes.

Key Topics and Features:

* Solid introduction to analytic number theory, including full proofs of Dirichlet’s Theorem and the Prime Number Theorem

* Solid treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals

* First treatment in book form of the AKS algorithm that shows that primality testing is of polynomial time

* Many interesting side topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers

The book’s user-friendly style, historical context, and wide range of exercises from simple to quite difficult (with solutions and hints provided for select ones) make it ideal for self study as well as classroom use. Intended for upper level undergraduates and beginning graduate students, 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 in the book.

Reviews

This book attempts the rather ambitious task of covering much of elementary, analytic and algebraic number theory in a bit over 300 pages. –MathSciNet


Table of contents (3 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-4541-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Number Theory
Book Subtitle
An Introduction via the Distribution of Primes
Authors
Copyright
2007
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4541-0
DOI
10.1007/978-0-8176-4541-0
Edition Number
1
Number of Pages
XVI, 342
Number of Illustrations and Tables
12 b/w illustrations
Topics