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An introduction to algebraic number theory 2nd ed

An introduction to algebraic number theory 2nd ed (7회 대출)

자료유형
단행본
개인저자
Ono, Takashi.
서명 / 저자사항
An introduction to algebraic number theory / Takashi Ono.
판사항
2nd ed.
발행사항
New York :   Plenum Press,   c1990.  
형태사항
xi, 223 p. : ill. ; 24 cm.
총서사항
The University series in mathematics.
ISBN
0306434369
일반주기
Translation of: Smuron josetsu.  
서지주기
Includes bibliographical references (p. 216-220) and index.
일반주제명
Algebraic number theory.
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100 1 0 ▼a Ono, Takashi.
240 1 0 ▼a Smuron josetsu. ▼l English
245 1 3 ▼a An introduction to algebraic number theory / ▼c Takashi Ono.
250 ▼a 2nd ed.
260 0 ▼a New York : ▼b Plenum Press, ▼c c1990.
300 ▼a xi, 223 p. : ▼b ill. ; ▼c 24 cm.
490 1 ▼a The University series in mathematics.
500 ▼a Translation of: Smuron josetsu.
504 ▼a Includes bibliographical references (p. 216-220) and index.
650 0 ▼a Algebraic number theory.
830 0 ▼a University series in mathematics (Plenum Press)

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컨텐츠정보

목차

CONTENTS
Notation and Conventions = xi
1. To the Gauss Reciprocity Law = 1
  1.1. Basic Facts = 2
  1.2. Modules in Z = 4
  1.3. Euclidean Algorithm and Continued Fractions = 8
  1.4. Continued-Fraction Expansion of Irrational Numbers = 12
  1.5. Concept of Groups = 16
  1.6. Subgroups and Quotient Groups = 21
  1.7. Ideals and Quotient Rings = 23
  1.8. Isomorphisms and Homomorphisms = 25
  1.9. Polynomial Rings = 28
  1.10. Primitive Roots = 30
  1.11. Algebraic Integers = 34
  1.12. Characters of Abelian Groups = 37
  1.13. The Gauss Reciprocity Law = 41
2. Basic Concepts of Algebraic Number Fields = 44
  2.1. Field Extensions = 44
  2.2. Galois Theory = 48
  2.3. Norm, Trace, and Discriminant = 53
  2.4. Gauss Sum and Jacobi Sum = 55
  2.5. Construction of a Regular l-gon = 58
  2.6. Subfields of the lth Cyclotomic Field = 60
  2.7. Cohomology of Cyclic Groups = 63
  2.8. Finite Fields = 68
  2.9. Ring of Integers, Ideals, and Discriminant = 69
  2.10. Fundamental Theorem of Ideal Theory = 74
  2.11. Residue Class Rings = 78
  2.12. Decomposition of Primes in Number Fields = 81
  2.13. Discriminant and Ramification = 86
  2.14. Hilbert Theory = 89
  2.15. Artin Map = 93
  2.16. Artin Maps of Subfields of the lth Cyclotomic Field = 97
  2.17. The Artin Map in Quadratic Fields = l00
3. Analytic Methods = 105
  3.1 Lattices in Rn = 105
  3.2. Minkowski's Theorem = 109
  3.3. Dirichlet's Unit Theorem = 113
  3.4. Pre-Zeta Functions = 119
  3.5. Dedekind Zeta Function = 123
  3.6. The mth Cyclotomic Field = 132
  3.7. Dirichlet L-Functions = 134
  3.8. Dirichlet's Theorem on Arithmetical Progressions = 140
4. The Ith Cyclotomic Fietd and Quadratic Fields = 143
  4.1. Determination of Gauss Sums = 144
  4.2. L-Functions and Gauss Sums = 149
  4.3. Class Numbers of Subfields of the lth Cyclotomic Field = 152
  4.4. Class Number of Q( l* ) = 155
  4.5. Ideal Class Groups of Quadratic Fields = 159
  4.6. Cohomology of Quadratic Fields = 166
  4.7. Gauss Genus Theory = 173
  4.8. Quadratic Irrationals = 179
  4.9. Real Quadratic Fields and Continued Fractions = 186
Answers and Hints to Exercises = 195
Notes = 210
  A. Peano Axioms = 210
  B. Fundamental Theorem of Algebra = 211
  C. Zorn's Lemma = 212
  D. Quadratic Fields and Quadratic Forms = 212
List of Mathematicians = 215
Bibliography = 216
  Comments on the Bibliography = 220
Index = 211

관련분야 신착자료

Aluffi, Paolo (2021)