A comprehensive course in number theory / Alan Baker

Von:

Baker, Alan, 1939-2018 [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: Cambridge : Cambridge University Press, 2012Beschreibung: 1 Online-Ressource (xv, 251 pages) : digital, PDF file(s)ISBN:

9781139093835

Schlagwörter:

Andere physische Formen: 9781107019010. | 9781107603790. | Erscheint auch als: A comprehensive course in number theory. Druck-Ausgabe Cambridge [u.a.] : Cambridge Univ. Press, 2012. XV, 251 S.DDC-Klassifikation:

512.7 23

MSC: MSC: *11-01 | 11Axx | 11Nxx | 11Pxx | 11Rxx | 11G05 | 11T71 | 11Dxx | 11H55 | 11Jxx | 11M06 | 11R04 | 11E16RVK: RVK: SK 180LOC-Klassifikation:

QA241

DOI: DOI: 10.1017/CBO9781139093835Online-Ressourcen:

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Zusammenfassung: Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studiesZusammenfassung: Machine generated contents note: Preface; Introduction; 1. Divisibility; 2. Arithmetical functions; 3. Congruences; 4. Quadratic residues; 5. Quadratic forms; 6. Diophantine approximation; 7. Quadratic fields; 8. Diophantine equations; 9. Factorization and primality testing; 10. Number fields; 11. Ideals; 12. Units and ideal classes; 13. Analytic number theory; 14. On the zeros of the zeta-function; 15. On the distribution of the primes; 16. The sieve and circle methods; 17. Elliptic curves; Bibliography; IndexPPN: PPN: 883411814Package identifier: Produktsigel: ZDB-20-CTM | ZDB-20-CBO

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