Introduction to Cyclotomic Fields

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Springer Science & Business Media, Jan 1, 1997 - Mathematics - 487 pages
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Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions, leading the reader to an understanding of modern research literature. Many exercises are included.
The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's f-invariant.
  

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Contents

III
1
IV
9
V
20
VI
30
VII
47
VIII
55
IX
59
X
63
XXXVIII
232
XXXIX
237
XL
252
XLI
264
XLII
265
XLIII
269
XLIV
277
XLV
285

XI
70
XII
77
XIII
87
XIV
93
XV
100
XVI
102
XVII
107
XVIII
113
XIX
117
XX
125
XXI
128
XXII
130
XXIII
143
XXIV
151
XXV
153
XXVI
159
XXVII
167
XXVIII
173
XXIX
185
XXX
188
XXXI
196
XXXII
205
XXXIII
206
XXXIV
211
XXXV
217
XXXVI
221
XXXVII
228
XLVI
292
XLVII
297
XLVIII
301
XLIX
310
L
319
LII
330
LV
332
LVI
339
LVII
346
LVIII
349
LIX
358
LX
367
LXI
371
LXIV
378
LXV
383
LXVI
389
LXVII
390
LXVIII
394
LXIX
405
LXX
408
LXXI
410
LXXII
416
LXXIII
420
LXXIV
479
LXXV
481
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Page iii - PREFACE TO THE SECOND EDITION Since the publication of the first edition of this book, "Definitions of Electrical Terms...
Page 453 - On the growth of the first factor of the class number of the prime cyclotomic field...
Page 475 - The determination of the imaginary abelian number fields with class number one.
Page 475 - On the rank of the p-divisor class group of Galois extensions of algebraic number fields. Kumamoto J.
Page 434 - On the trace of the ring of integers of an abelian number field, Acta Arith., 62, 1992, 383-389.

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