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

Gespeichert in:
Weitere Titel:
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 unit theorem, I
A case study: Units in $\mathbb {Z}[\sqrt [3]{2}]$ and the Diophantine equation $X^3-2Y^3=\pm 1$
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
1. Verfasser:
Pollack, Paul
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
Providence, Rhode Island : American Mathematical Society, [2017]
Umfang:
1 online resource (ix, 316 pages : illustrations)
Mode of access : World Wide Web
Format Details:
Mode of access : World Wide Web
Bibliografie:
Includes bibliographical references and index.
Schriftenreihe:
The Student Mathematical Library,
Sekundärform:
Publikations­art: Electronic reproduction.
Verlag: Providence, Rhode Island :: American Mathematical Society.
Publikations­datum: 2017
ISBN:
9781470441258 (online)
ISSN:
1520-9121
DOI:
10.1090/stml/084
Zugangseinschränkungen:
Access is restricted to licensed institutions
Schlagworte:
Algebraic number theory.
Number theory > Algebraic number theory: global fields > Algebraic number theory: global fields.
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