Springer Undergraduate Mathematics Series

Algebraic Number Theory

Authors: Jarvis, Frazer

  • Provides a self-contained and easy-to-read introduction to algebraic number theory, with minimal algebraic prerequisites
  • Introduces the theory of ideals in a historical context, through the study of the failure of unique factorisation in number fields
  • Introduces the number field sieve at a level suitable for undergraduates
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eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-319-07545-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-07544-0
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  • Usually dispatched within 3 to 5 business days.
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About this Textbook

This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.

The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

About the authors

Frazer Jarvis obtained his PhD from the University of Cambridge under the supervision of Richard Taylor in 1995. After postdoctoral periods in Strasbourg, Durham and Oxford, he has been a lecturer at Sheffield since 1998. His research has focused on modular forms and Galois representations over totally real fields, and he is currently interested in GSp(4).

Reviews

“Undergraduate mathematics students need both to develop facility with numerical and symbolic calculation and comfort with abstraction. Algebraic number theory offers an ideal context for encountering the synthesis of these goals. One could compile a shelf of graduate-level expositions of algebraic number theory, and another shelf of undergraduate general number theory texts that culminate with a first exposure to it. … Summing Up: Highly recommended. Upper-division undergraduates.” (D. V. Feldman, Choice, Vol. 52 (8), April, 2015)

“In this book, the author leads the readers from the theorem of unique factorization in elementary number theory to central results in algebraic number theory. … This book is designed for being used in undergraduate courses in algebraic number theory; the clarity of the exposition and the wealth of examples and exercises (with hints and solutions) also make it suitable for self-study and reading courses.” (Franz Lemmermeyer, zbMATH, Vol. 1303, 2015)

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Table of contents (2 chapters)

  • Unique Factorisation in the Natural Numbers

    Frazer Jarvis

    Pages 1-16

    Preview Buy Chapter 30,19 €
  • Lattices and Geometrical Methods

    Frazer Jarvis

    Pages 149-168

    Preview Buy Chapter 30,19 €

Buy this book

eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-319-07545-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-07544-0
  • 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
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Number Theory
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-07545-7
DOI
10.1007/978-3-319-07545-7
Softcover ISBN
978-3-319-07544-0
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XIII, 292
Number of Illustrations and Tables
3 b/w illustrations
Topics