Author | Ribenboim, Paulo. author |
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Title | Classical Theory of Algebraic Numbers [electronic resource] / by Paulo Ribenboim |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-0-387-21690-4 |
Descript | XXIV, 682 p. online resource |
Unique Factorization Domains, Ideals, and Principal Ideal Domains -- Commutative Fields -- One -- Residue Classes -- Quadratic Residues -- Two -- Algebraic Integers -- Integral Basis, Discriminant -- The Decomposition of Ideals -- The Norm and Classes of Ideals -- Estimates for the Discriminant -- Units -- Extension of Ideals -- Algebraic Interlude -- The Relative Trace, Norm, Discriminant, and Different -- The Decomposition of Prime Ideals in Galois Extensions -- The Fundamental Theorem of Abelian Extensions -- Complements and Miscellaneous Numerical Examples -- Three -- Local Methods for Cyclotomic Fields -- Bernoulli Numbers -- Fermatโs Last Theorem for Regular Prime Exponents -- More on Cyclotomic Extensions -- Four -- Characters and Gaussian Sums -- Zeta-Functions and L-Series -- The Dedekind Zeta-Function -- Primes in Arithmetic Progressions -- The Frobenius Automorphism and the Splitting of Prime Ideals -- Class Numbers of Quadratic Fields -- Class Number of Cyclotomic Fields -- Miscellaneous Results About the Class Number of Quadratic Fields -- Miscellaneous Results About the Class Number of Cyclotomic Fields