A Course in Computational Algebraic Number Theory

Front Cover
Springer Science & Business Media, Jan 1, 1993 - Computers - 534 pages
2 Reviews
With the advent of powerful computing tools and numerous advances in math ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
  

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Contents

I
1
II
2
III
5
IV
6
V
8
VI
12
VIII
16
IX
19
CXXIII
288
CXXIV
289
CXXV
291
CXXVI
295
CXXVIII
297
CXXIX
298
CXXX
303
CXXXI
305

X
21
XI
24
XII
27
XIII
31
XIV
32
XV
34
XVI
36
XVII
38
XIX
39
XX
41
XXI
42
XXII
46
XXIII
47
XXIV
48
XXV
50
XXVI
53
XXVII
57
XXVIII
60
XXIX
62
XXX
64
XXXI
66
XXXII
67
XXXIII
73
XXXIV
75
XXXV
79
XXXVI
82
XXXVII
84
XXXVIII
90
XXXIX
92
XL
95
XLI
97
XLII
100
XLIII
103
XLIV
106
XLV
109
XLVI
110
XLVII
111
XLVIII
113
XLIX
114
L
116
LI
117
LII
118
LIII
119
LIV
123
LV
124
LVI
125
LVII
126
LVIII
127
LIX
133
LX
134
LXI
135
LXII
137
LXIII
139
LXIV
141
LXV
142
LXVI
143
LXVII
146
LXVIII
148
LXIX
153
LXX
154
LXXI
158
LXXIII
159
LXXIV
160
LXXV
161
LXXVI
162
LXXVII
165
LXXVIII
168
LXXIX
174
LXXXI
175
LXXXII
177
LXXXIII
179
LXXXIV
181
LXXXV
186
LXXXVI
188
LXXXVII
190
LXXXVIII
196
XC
199
XCI
201
XCII
204
XCIII
207
XCIV
209
XCV
217
XCVII
223
XCVIII
225
XCIX
231
CI
234
CII
237
CIII
240
CV
243
CVI
250
CVII
252
CIX
255
CX
260
CXI
262
CXIII
266
CXIV
268
CXV
269
CXVII
271
CXVIII
278
CXIX
279
CXX
283
CXXI
285
CXXII
287
CXXXII
308
CXXXIII
311
CXXXIV
312
CXXXV
313
CXXXVI
315
CXXXVII
317
CXXXVIII
318
CXXXIX
320
CXL
322
CXLI
325
CXLIII
328
CXLIV
329
CXLV
331
CXLVI
333
CXLVII
334
CXLVIII
336
CXLIX
343
CL
347
CLI
351
CLII
352
CLIV
354
CLV
357
CLVI
358
CLVII
360
CLVIII
362
CLIX
367
CLX
369
CLXI
372
CLXII
376
CLXIII
377
CLXIV
379
CLXV
381
CLXVI
384
CLXVII
385
CLXVIII
386
CLXIX
387
CLXX
388
CLXXI
390
CLXXII
392
CLXXIII
394
CLXXV
399
CLXXVI
403
CLXXVII
406
CLXXVIII
410
CLXXIX
413
CLXXX
414
CLXXXI
415
CLXXXII
416
CLXXXIII
417
CLXXXIV
419
CLXXXV
421
CLXXXVI
423
CLXXXVIII
424
CLXXXIX
425
CXC
426
CXCI
427
CXCII
429
CXCIII
430
CXCIV
433
CXCV
434
CXCVI
438
CXCVII
439
CXCVIII
440
CXCIX
441
CC
442
CCI
445
CCII
446
CCIV
448
CCV
450
CCVI
455
CCVII
457
CCVIII
463
CCIX
465
CCX
467
CCXII
471
CCXIII
475
CCXIV
477
CCXV
481
CCXVI
482
CCXVII
484
CCXVIII
485
CCXIX
487
CCXX
489
CCXXI
490
CCXXII
491
CCXXIII
492
CCXXIV
494
CCXXV
495
CCXXVI
496
CCXXVII
500
CCXXVIII
501
CCXXIX
503
CCXXX
504
CCXXXI
507
CCXXXII
513
CCXXXIII
515
CCXXXIV
519
CCXXXV
521
CCXXXVI
524
CCXXXVII
527
CCXXXVIII
540
CCXXXIX
547
Copyright

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Page 532 - AOL Atkin. The number of points on an elliptic curve modulo a prime. Preprint, 1988. 3. AOL Atkin. The number of points on an elliptic curve modulo a prime (ii).
Page 532 - Notes on elliptic curves I." J. Reine Angew. Math. 212 (1963), pp. 7-25. [Ca] JW CASSELS, "The rational solutions of the diophantine equation/ = x3 - D,
Page 532 - J. Buchmann, On the computation of units and class numbers by a generalization of Lagrange's algorithm, J. Number Theory 26 (1987), 8-30.

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About the author (1993)

Cohen, Universite de Bordeaux 1, Talence, France.

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