: arithmetic beyond Z Pollack, Paul creator Pollack, Paul text Providence, Rhode Island : AMS, American Mathematical Society ©2017 monographic eng

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ix, 316 pages : illustrations ; 22 cm. Getting our feet wetCast of charactersQuadratic number fields: First stepsParadise lost--and foundEuclidean quadratic fieldsIdeal theory for quadratic fieldsPrime ideals in quadratic number ringsUnits in quadratic number ringsA touch of classMeasuring the failure of unique factorizationEuler's prime-producing polynomial and the criterion of Frobenius-RabinowitschInterlude: Lattice pointsBack to basics: Starting over with arbitrary number fieldsIntegral bases: From theory to practice, and backIdeal theory in general number ringsFiniteness of the class group and the arithmetic of $\overline{\mathbb{Z}}$Prime decomposition in general number ringsDirichlet's units theorem, IA case study: Units in $\mathbb{Z}[\sqrt[3]{2}]$ and the Diophantine equation $X^3-2Y^3=\pm1$Dirichlet's units theorem, IIMore Minkowski magic, with a cameo appearance by HermiteDedekind's discriminant theoremThe quadratic Gauss sumIdeal density in quadratic number fieldsDirichlet's class number formulaThree miraculous appearances of quadratic class numbersIndex. / Paul Pollack Mathematics Algebra Algebraic number theory Number theory -- Algebraic number theory: global fields -- Algebraic number theory: global fields 512.74 POL 978147044890 191022 20191022140104.0