A Classical Introduction to Modern Number TheoryBridging 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. |
Contents
CHAPTER | 1 |
CHAPTER | 14 |
Applications of Unique Factorization | 17 |
Copyright | |
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A Classical Introduction to Modern Number Theory Kenneth Ireland,Michael Ira Rosen Limited preview - 1990 |
Common terms and phrases
a₁ algebraic integers algebraic number field assume b₁ Bernoulli numbers biquadratic Chapter character of order class number coefficients complex numbers congruence conjecture consider Corollary defined definition degree denote Dirichlet character divides divisors Eisenstein equation Exercise Fermat's finite field Galois Gauss sums Hecke character hypersurface implies infinitely many primes integral solution irreducible polynomials Jacobi sums Kummer Legendre symbol Lemma Let F monic polynomial multiplicative nontrivial nonzero number of points number of solutions number theory odd prime P₁ points at infinity positive integer primary prime ideal prime number primitive root PROOF Proposition prove q elements quadratic reciprocity quadratic residue reciprocity laws relatively prime result follows Riemann ring of integers root of unity Section solvable Suppose Theorem Z/pZ zero zeta function