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ireland kenneth; rosen michael - a classical introduction to modern number theory

A Classical Introduction to Modern Number Theory

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 08/1998
Edizione: 2nd ed. 1990. Corr. 5th printing 1998





Trama

Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.




Sommario

1: Unique Factorization. 2: Applications of Unique Factorization. 3: Congruence. 4: The Structure of U. 5: Quadratic Reciprocity. 6: Quadratic Gauss Sums. 7: Finite Fields. 8: Gauss and Jacobi Sums. 9: Cubic and Biquadratic Reciprocity. 10: Equations over Finite Fields. 11: The Zeta Function. 12: Algebraic Number Theory. 13: Quadratic and Cyclotomic Fields. 14: The Stickelberger Relation and the Eisenstein Reciprocity Law. 15: Bernoulli Numbers. 16: Dirichlet L-functions. 17: Diophantine Equations. 18: Elliptic Curves. 19: The Mordell-Weil Theorem. 20: New Progress in Arithmetic Geometry.










Altre Informazioni

ISBN:

9780387973296

Condizione: Nuovo
Collana: Graduate Texts in Mathematics
Dimensioni: 235 x 155 mm Ø 817 gr
Formato: Copertina rigida
Illustration Notes:XIV, 394 p.
Pagine Arabe: 394
Pagine Romane: xiv


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