Algebraic Curves Over Finite Fields

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Cambridge University Press, Oct 14, 1993 - Mathematics - 260 pages
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In this tract, Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves. Among the applications considered are: the problem of counting the number of solutions of equations over finite fields; Bombieri's proof of the Reimann hypothesis for function fields, with consequences for the estimation of exponential sums in one variable; Goppa's theory of error-correcting codes constructed from linear systems on algebraic curves; there is also a new proof of the TsfasmanSHVladutSHZink theorem. The prerequisites needed to follow this book are few, and it can be used for graduate courses for mathematics students. Electrical engineers who need to understand the modern developments in the theory of error-correcting codes will also benefit from studying this work.
 

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Contents

II
1
III
4
IV
6
V
8
VI
10
VII
11
VIII
16
IX
17
XLVI
137
XLVII
138
XLVIII
140
L
141
LI
147
LII
153
LIII
154
LIV
155

X
18
XI
20
XII
23
XIII
26
XIV
27
XV
28
XVI
31
XVII
32
XVIII
36
XIX
38
XX
42
XXI
46
XXII
47
XXIII
48
XXIV
52
XXV
57
XXVI
59
XXVII
69
XXVIII
70
XXIX
76
XXX
85
XXXI
87
XXXII
89
XXXIII
91
XXXIV
92
XXXV
95
XXXVI
97
XXXVII
98
XXXVIII
108
XXXIX
111
XL
113
XLI
114
XLII
122
XLIII
127
XLIV
131
XLV
136
LV
160
LVI
162
LVII
164
LVIII
170
LIX
171
LX
176
LXI
178
LXII
179
LXIII
184
LXIV
188
LXV
189
LXVI
198
LXVII
203
LXVIII
208
LXIX
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LXX
211
LXXI
212
LXXII
213
LXXIII
214
LXXIV
216
LXXV
217
LXXVI
220
LXXVII
221
LXXVIII
222
LXXIX
223
LXXX
226
LXXXI
227
LXXXII
230
LXXXIII
231
LXXXIV
233
LXXXV
234
LXXXVI
235
LXXXVII
239
LXXXVIII
245
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About the author (1993)

Moreno is Professor of Mathematics, Baruch College, City University of New York.

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