Introduction to Cyclotomic Fields

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Springer Science & Business Media, 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
3
V
11
VII
22
IX
32
XI
49
XIII
57
XIV
61
XV
65
L
234
LII
239
LIII
254
LIV
266
LVI
267
LVII
271
LVIII
279
LIX
287

XVI
72
XVII
79
XVIII
89
XX
95
XXI
102
XXII
104
XXIII
109
XXIV
115
XXVII
119
XXVIII
127
XXIX
130
XXX
132
XXXI
145
XXXIII
153
XXXIV
155
XXXV
161
XXXVI
169
XXXIX
175
XL
187
XLII
190
XLIII
198
XLIV
207
XLV
208
XLVI
213
XLVII
219
XLVIII
223
XLIX
230
LX
294
LXI
299
LXII
303
LXIII
314
LXIV
323
LXVI
334
LXIX
336
LXX
343
LXXI
350
LXXII
353
LXXIII
362
LXXIV
371
LXXV
375
LXXVII
382
LXXVIII
387
LXXIX
393
LXXX
394
LXXXI
398
LXXXII
409
LXXXIV
412
LXXXV
414
LXXXVI
422
LXXXVII
426
LXXXVIII
485
LXXXIX
487
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Page v - PREFACE TO THE SECOND EDITION Since the publication of the first edition of this book, "Definitions of Electrical Terms...
Page 459 - On the growth of the first factor of the class number of the prime cyclotomic field...
Page 424 - On a cyclic determinant and the first factor of the class number of the cyclotomic field, ks.
Page 481 - The determination of the imaginary abelian number fields with class number one.
Page 481 - On the rank of the p-divisor class group of Galois extensions of algebraic number fields. Kumamoto J.

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