A Classical Introduction to Modern Number TheorySpringer-Verlag, 1982 - 341 pages 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. |
Table des matières
CHAPTER | 1 |
Proof of the Law of Cubic Reciprocity | 4 |
CHAPTER | 14 |
Droits d'auteur | |
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Autres éditions - Tout afficher
A Classical Introduction to Modern Number Theory Kenneth Ireland,Michael Ira Rosen Aperçu limité - 1990 |
Expressions et termes fréquents
a₁ algebraic integers algebraic number field assume b₁ Bernoulli numbers biquadratic Chapter character of order class number coefficients complex numbers congruence conjecture consider Corollary cubic curve cyclic defined definition degree denote Dirichlet character divides divisor Eisenstein equation Exercise Fermat's finite field Galois Gauss sums implies infinitely many primes irreducible polynomials Jacobi sums law of quadratic Legendre symbol Lemma Let F monic polynomial multiplicative nonresidue nontrivial nonzero number of points number of solutions number theory odd prime P₁ positive integer prime ideal prime number PROOF Proposition prove quadratic reciprocity quadratic residue quadratic residue mod r₁ reciprocity law relatively prime result follows ring of integers root of unity Section solvable square-free Suppose Theorem x₁ Z/mZ Z/pZ zero zeta function