A Brief guide to algebraic number theory

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A Brief guide to algebraic number theory / H. P. F. Swinnerton-Dyer

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2001
形態:: ix, 146 p. ; 24 cm
シリーズ名:: London Mathematical Society student texts ; 50 <BA00194352>
著者名:: Swinnerton-Dyer, H. P. F. <DA09391596>
ISBN:: 9780521802925 [052180292X] (: hbk)
9780521004237 [0521004233] (: pbk)
書誌ID:: BA50677449

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注記:

Includes index

言語:

英語

目次情報:

Preface

Numbers and Ideals / 1：

The ring of integers

Ideals and factorization / 2：

Embedding in the complex numbers / 3：

Change of fields / 4：

Normal extensions / 5：

Valuations

Valuations and completions / 6：

Field extensions and ramification / 7：

The Different / 8：

Ideles and Adeles / 9：

Special fields

Quadratic fields / 10：

Pure cubic fields / 11：

Biquadratic fields / 12：

Cyclotomic fields / 13：

Class numbers of cyclotomic fields / 13.1：

Fermat's Last Theorem / 13.2：

Analytic methods

Zeta functions and L-series / 14：

Analytic continuation and the functional equation / 15：

Density theorems / 16：

Class Field Theory

The classical theory / 17：

Chevalley's reformulation / 18：

Reciprocity theorems / 19：

The Kronecker-Weber Theorem / 20：

Appendix

Prerequisites / A1：

Finitely generated abelian groups and lattices / A1.1：

Norms and Traces / A1.2：

Haar measure / A1.3：

Additional topics / A2：

Characters and duality / A2.1：

Fourier transforms / A2.2：

Galois theory for infinite extensions / A2.3：

Exercises

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