A conversational introduction to algebraic number theory : arithmetic beyond Z / Paul Pollack

Author:: Pollack, Paul, 1980-
Published:: Providence, Rhode Island : American Mathematical Society, [2017]
Physical Description:: ix, 316 pages ; 22 cm.

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Series:

Student mathematical library ; volume 84

Contents:

Machine generated contents note: ch. 1 Getting our feet wet -- ch. 2 Cast of characters -- ch. 3 Quadratic number fields: First steps -- ch. 4 Paradise lost --- and found -- ch. 5 Euclidean quadratic fields -- ch. 6 Ideal theory for quadratic fields -- ch. 7 Prime ideals in quadratic number rings -- ch. 8 Units in quadratic number rings -- ch. 9 A touch of class -- ch. 10 Measuring the failure of unique factorization -- ch. 11 Euler's prime-producing polynomial and the criterion of Frobenius-Rabinowitsch -- ch. 12 Interlude: Lattice points -- ch. 13 Back to basics: Starting over with arbitrary number fields -- ch. 14 Integral bases: From theory to practice, and back -- ch. 15 Ideal theory in general number rings -- ch. 16 Finiteness of the class group and the arithmetic of Z -- ch. 17 Prime decomposition in general number rings -- ch. 18 Dirichlet's unit theorem, I -- ch. 19 A case study: Units in Z[2[√]/2] and the Diophantine equation X3 - 2Y3 = ±1 -- ch. 20 Dirichlet's unit theorem, II -- ch. 21 More Minkowski magic, with a cameo appearance by Hermite -- ch. 22 Dedekind's discriminant theorem -- ch. 23 The quadratic Gauss sum -- ch. 24 Ideal density in quadratic number fields -- ch. 25 Dirichlet's class number formula -- ch. 26 Three miraculous appearances of quadratic class numbers.

Subject(s):

ISBN:

9781470436537 paperback alkaline paper
1470436531 paperback alkaline paper

Bibliography Note:

Includes bibliographical references and index.

View MARC record | catkey: 21047660