Frazer Jarvis: Algebraic Number Theory

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Cover: 9783319075440 | Algebraic Number Theory | Frazer Jarvis | Taschenbuch | Paperback

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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).

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

Unique factorisation in the natural numbers.- Number fields.- Fields, discriminants and integral bases.- Ideals.- Prime ideals and unique factorisation.- Imaginary quadratic fields.- Lattices and geometrical methods.- Other fields of small degree.- Cyclotomic fields and the Fermat equation.- Analytic methods.- The number field sieve.

Erscheinungsjahr:	2014
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	308
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xiii 292 S. 3 s/w Illustr. 292 p. 3 illus.
ISBN-13:	9783319075440
ISBN-10:	3319075446
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Jarvis, Frazer
Auflage:	2014
Hersteller:	Springer International Publishing Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 17 mm
Von/Mit:	Frazer Jarvis
Erscheinungsdatum:	04.07.2014
Gewicht:	0,47 kg

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