A classical introduction to modern number theory
著者
書誌事項
A classical introduction to modern number theory
（Graduate texts in mathematics, 84）
Springer-Verlag, c1990
2nd ed
- : us
- : gw
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注記
Bibliography: p. 375-384
Includes index
corr. 2nd printing, 1993
corr. 5nd printing, 1998
内容説明・目次
- 巻冊次
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: us ISBN 9780387973296
内容説明
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.
目次
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.
- 巻冊次
-
: gw ISBN 9783540973294
内容説明
Bridging the gap between elementary number theory and the systematic study of advanced topics. This text requires a familiarity with basic abstract algebra. Historical development is stressed throughout, along with coverage of significant results with comparatively elementary proofs, some of them new. An bibliography and several exercises are also included and this edition offers two new chapters that give a complete proof of Mordell's fundamental theorem and an overview of Flating's proof of the Mordell conjecture. Also included is material on the recent progress on the arithmetic of elliptic curves.
目次
Contents: Unique Factorization.- Applications of Unique Factorization.- Congruence.- The Structure of U(Z/nZ).- Quadratic Reciprocity.- Quadratic Gauss Sums.- Finite Fields.- Gauss and Jacobi Sums.- Cubic and Biquadratic Reciprocity.- Equations Over Finite Fields.- The Zeta Function.- Algebraic Number Theory.- Quadratic and Cyclotomic Fields.- The Stickelberger Relation and the Eisenstein Reciprocity Law.- Bernoulli Numbers.- Dirichlet L-Functions.- Diophantine Equations.- Elliptic Curves.- The Mordell-Weil Theorem.- New Progress in Arithmetic Geometry.- Selected Hints for the Exercises.
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