ENGLISH

Algebraic Number Theory

By Frazer Jarvis (auth.)

Book information

Publisher
Springer International Publishing
Year
2014
ISBN
978-3-319-07544-0, 978-3-319-07545-7
DOI
10.1007/978-3-319-07545-7
Language
english
Format
PDF
Filesize
3 MB (2848405 bytes)
Series
Springer Undergraduate Mathematics Series
Edition
1
Pages
292\298
Time added
2014-11-10 20:00:00
Number Theory; Field Theory and Polynomials

Description

The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes 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.

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