This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
Rezensionen / Stimmen
From the reviews of the second edition: K. Ireland and M. Rosen A Classical Introduction to Modern Number Theory "Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution." - MATHEMATICAL REVIEWS "This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. ... for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvea, MathDL, January, 2006)
Produkt-Info
Reihe
Auflage
2nd ed. 1990. Corr. 5th printing
Sprache
Verlagsort
Zielgruppe
Editions-Typ
Produkt-Hinweis
Illustrationen
Maße
Höhe: 243 mm
Breite: 166 mm
Dicke: 29 mm
Gewicht
ISBN-13
978-0-387-97329-6 (9780387973296)
DOI
10.1007/978-1-4757-2103-4
Schweitzer Klassifikation
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.
