A Classical Introduction to Modern Number TheorySpringer-Verlag, 1982 - 341 páginas 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. |
Conteúdo
CHAPTER | 1 |
CHAPTER | 14 |
Applications of Unique Factorization | 17 |
Direitos autorais | |
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Outras edições - Ver todos
A Classical Introduction to Modern Number Theory Kenneth Ireland,Michael Ira Rosen Visualização parcial - 1990 |
A Classical Introduction to Modern Number Theory Kenneth Ireland,Michael Rosen Visualização parcial - 2013 |
Termos e frases comuns
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