Number Theory

An Introduction via the Density of Primes

Authors: Fine, Benjamin, Rosenberger, Gerhard

Free Preview
  • 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
  • One of the few books to include the AKS algorithm that shows that primality testing is one of polynomial time
  • Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers
see more benefits

Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-3-319-43875-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-43873-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-82931-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

Benjamin Fine, PhD, is Professor of Mathematics at Fairfield University, CT, USA.

Gerhard Rosenberger, PhD, is Professor (retired) at Dortmund University of Technology, Germany.

Reviews

“In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. … Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)

“The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. … a good text for an introductory course … .” (Allen Stenger, MAA Reviews, maa.org, November, 2016)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-3-319-43875-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-43873-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-82931-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Number Theory
Book Subtitle
An Introduction via the Density of Primes
Authors
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-43875-7
DOI
10.1007/978-3-319-43875-7
Hardcover ISBN
978-3-319-43873-3
Softcover ISBN
978-3-319-82931-9
Edition Number
2
Number of Pages
XIII, 413
Number of Illustrations
11 b/w illustrations, 1 illustrations in colour
Topics