01862nam a22002297a 4500 55795 55795 20191022140104.0 191022b ||||| |||| 00| 0 eng d 978147044890 512.74 POL Pollack, Paul, A conversational introduction to algebraic number theory : arithmetic beyond Z / Paul Pollack Providence, Rhode Island : AMS, American Mathematical Society, ©2017 ix, 316 pages : illustrations ; 22 cm. Student mathematical library, v. 84. 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. Mathematics Algebra Algebraic number theory. Number theory -- Algebraic number theory: global fields -- Algebraic number theory: global fields. Pollack, Paul, MDL 0 0 ddc 0 0 MDL SNUL 2019-10-22 0 512.74 POL M028 2019-10-22 00:00:00 2019-10-22 MDL