Lectures on the Theory of Algebraic Numbers

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Springer Science & Business Media, Dec 4, 1981 - Mathematics - 239 pages
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. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.
 

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Contents

I
1
II
6
III
10
IV
13
V
16
VI
20
VII
22
VIII
24
XXXIV
108
XXXV
113
XXXVI
116
XXXVII
122
XXXVIII
125
XXXIX
132
XL
139
XLI
143

IX
28
X
30
XI
34
XII
40
XIII
42
XIV
45
XV
48
XVI
50
XVII
54
XVIII
57
XIX
59
XX
63
XXI
68
XXII
71
XXIII
73
XXIV
77
XXV
83
XXVI
85
XXVII
87
XXVIII
91
XXIX
94
XXX
98
XXXI
100
XXXII
102
XXXIII
105
XLII
144
XLIII
148
XLIV
155
XLV
159
XLVI
163
XLVII
168
XLVIII
172
XLIX
176
L
179
LI
181
LII
184
LIII
187
LIV
195
LV
200
LVI
205
LVII
210
LVIII
215
LIX
217
LX
224
LXI
227
LXII
230
LXIII
234
LXIV
238
LXV
239
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