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Author:   Paul Pollack
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.389kg
ISBN:  

9781470436537

ISBN 10:   1470436531
Pages:   312
Publication Date:   30 September 2017
Audience:   College/higher education ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Getting our feet wet Cast of characters Quadratic number fields: First steps Paradise lost--and found Euclidean quadratic fields Ideal theory for 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, and back Ideal theory in general number rings Finiteness of the class group and the arithmetic of $\overline{\mathbb{Z}}$ Prime decomposition in general number rings Dirichlet's units theorem, I A case study: Units in $\mathbb{Z}[\sqrt[3]{2}]$ and the Diophantine equation $X^3-2Y^3=\pm1$ Dirichlet's units 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 Index.

Reviews

This is a lucid, clearly written text, with a thoughtful choice and arrangement of topics, presented with contagious enthusiasm. It is a welcome addition to the existing literature on the subject. - Charles Helou, Mathematical Reviews

"This is a lucid, clearly written text, with a thoughtful choice and arrangement of topics, presented with contagious enthusiasm. It is a welcome addition to the existing literature on the subject."" — Charles Helou, Mathematical Reviews"

Author Information

Paul Pollack, University of Georgia, Athens, GA.

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