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Local fields

Local fields (Loan 3 times)

Material type
단행본
Personal Author
Cassels, J. W. S. (John William Scott)
Title Statement
Local fields / J.W.S. Cassels.
Publication, Distribution, etc
Cambridge [Cambridgeshire] ;   New York :   Cambridge University Press,   c1986.  
Physical Medium
xiv, 360 p. : ill. ; 24 cm.
Series Statement
London mathematical society student texts ;3.
ISBN
0521304849 0521315255 (pbk.)
Bibliography, Etc. Note
Includes bibliography(p. 352-357) and index.
Subject Added Entry-Topical Term
Local fields (Algebra).
000 00776camuuu200241 a 4500
001 000000902890
005 19990111165808.0
008 850628s1986 enka b 00110 eng
010 ▼a 85047934
020 ▼a 0521304849
020 ▼a 0521315255 (pbk.)
040 ▼a DLC ▼c DLC ▼d 244002
049 0 ▼l 452032324
050 0 0 ▼a QA247 ▼b .C34 1986
082 0 0 ▼a 512/.3 ▼2 19
090 ▼a 512.3 ▼b C344L
100 1 ▼a Cassels, J. W. S. ▼q (John William Scott)
245 1 0 ▼a Local fields / ▼c J.W.S. Cassels.
260 ▼a Cambridge [Cambridgeshire] ; ▼a New York : ▼b Cambridge University Press, ▼c c1986.
300 ▼a xiv, 360 p. : ▼b ill. ; ▼c 24 cm.
440 0 ▼a London mathematical society student texts ; ▼v 3.
504 ▼a Includes bibliography(p. 352-357) and index.
650 0 ▼a Local fields (Algebra).

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Sejong Academic Information Center/Science & Technology/ Call Number 512.3 C344L Accession No. 452032324 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

CONTENTS
Preface = ⅴ
Leirfaden = xiii
Notational conventions = xiv
Chapter 1. Introduction. = 1
  1. Valuations = 1
  2. Remarks = 4
  3. An application = 6
Chapter 2. General properties = 12
  1. Definitions and basics = 12
  2. Valuations on the rationals = 16
  3. Independence of valuations = 18
  4. Completion = 23
  5. Formal series and a theorem of Eisenstein = 26
Chapter 3. Archimedean valuations = 33
  1. Introduction = 33
  2. Some lemmas = 34
  3. Completion of proof = 38
Chapter 4. Non archimedean valuations. Simple properties = 41
  1. Definitions and basics = 41
  2. An application to finite groups of rational matrices = 46
  3. Hensel's lemma = 49
  3. bis. Application to diophantine equations = 53
  4. Elementary analysis = 59
  5. A useful expansion = 64
  6. An application to recurrent sequences = 67
Chapter 5. Embedding theorem = 82
  1. Introduction = 82
  2. Three lemmas = 82
  3. Proof of theorem = 84
  4. Application. A theorem of Selberg = 87
  5. Application. The theorem of Mahler and Lech = 88
Chapter 6. Transcendental extensions. Factorization = 92
  1. Introduction = 92
  2. Gauss' lemma and Eisenstein irreducibility = 95
  3. Newton polygon = 98
  4. Factorization of pure polynomials = 105
  5. "Weierstrass" preparation theorem = 107
Chapter 7. Algebraic extensions (complete fields) = 114
  1. Introduction = 114
  2. Uniqueness = 115
  3. Existence and corollaries = 118
  4. Residue class fields = 120
  5. Ramification = 123
  6. Discriminants = 128
  7. Completely ramified extensions = 133
  8. Action of galois = 134
Chapter 8. p-adic fields = 144
  1. Introduction = 144
  2. Unramified extensions = 147
  3. Non-completeness of Q ? p = 149
  4. "Kronecker-Weber" theorem = 151
Chapter 9. Algebraic extensions (incomplete fields) = 165
  1. Introduction 165
  2. Proof of theorem : norm and trace = 167
  3. Integers and discriminants = 170
  4. Application to cyclotomic fields = 174
  5. Action of galois = 176
  6. Application. Quadratic reciprocity = 178
Chapter 10. Algebraic number fields = 189
  1. Introduction = 189
  2. Product formula = 190
  3. Algebraic integers = 191
  4. Strong approximation theorem = 196
  5. Divisors. Relation to ideal theory = 197
  6. Existence theorems = 203
  7. Finiteness of the class number = 208
  8. The unit group = 211
  9. Application to diophantine equations. Rational solutions = 220
  10. Application to diophantine equations. Integral solutions = 222
    10. bis. Application to diophantine equations. Integral solutions. (contd) = 228
  11. The discriminant = 231
  12. The Kronecker-Weber theorem = 235
  13. Statistics of prime decomposition = 237
Chapter 11. Diophantine equations = 250
  1. Introduction = 250
  2. Basse Principle for ternary quadratics = 252
  3. Curves of genus 1. Generalities = 257
  4. Curves of genus 1. A special case = 261
Chapter 12. Advanced analysis = 280
  1. Introduction = 280
  2. Elementary functions = 280
  3. Analytic continuation = 285
  4. Measure on Zp = 288
  5. The zeta function = 291
  6. L-functions = 296
  7. Mahler's expansion = 306
Chapter 13. A theorem of Borel and Dwork = 313
  1. Introduction = 313
  2. Some lemmas = 314
  3. Proof = 317
Appendix A. Resultants and discriminants = 320
Appendix B. Norms, traces and characteristic polynomials = 325
Appendix C. Minkowski's convex body theorem = 331
Appendix D. Solution of equations in finite fields = 337
Appendix E. Zeta and L-functions at negative integers = 347
Appendix F. Calculation of exponentials = 350
References = 352
Index = 358