A conversational introduction to algebraic number theory arithmetic beyond Z - Pollack, Paul (Providence, Rhode Island American Mathematical Society, 2017)
Getting our feet wet -- Cast of characters -- Quadratic numbers fields : first stes -- Paradise lost--and found -- Euclidean quadratic fields -- Prime ideals in quadratic number rings -- Units in quadratic number rings -- A touch of class -- Measuring the failure of unique factorization -- Euler's prime-producing polynomial and the criterion of Frobenius-Rabinowitsch -- Interlude : Lattice points -- Back to basics : starting over with arbitrary number fields -- Integral bases : from theory to practice, an dback -- Ideal theory in general number rings -- Finiteness of the class group and the arithmetic of Z -- Prime decomposition in general number rings -- Dirichlet's unit theorem, I -- A case study : units in \Z[√[3]2] and the Diophantine equation X³-2Y³=±1 -- Dirichlet's unit theorem, II -- More Minkowski magic, with a cameo appearance by Hermite -- Dedekind's discriminant theorem -- The quadratic Gauss sum -- Ideal density in quadratic number fields -- Dirichlet's class number formula -- Three miraculous appearances of quadratic class numbers.
Includes bibliographical references and index.
Keywords: Algebraic number theory; Number theory -- Algebraic number theory