The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
Recenzijos
The book is a new masterpiece in the series of Wladislaw Narkiewiczs books that are favourites of all researchers in number theory. The book is truly recommended to all number theorists. (Istvįn Gaįl, zbMath 1416.11003, 2019)
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1 The Birth of Algebraic Number Theory |
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1 | (62) |
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1 | (15) |
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1 | (1) |
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2 | (10) |
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12 | (4) |
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16 | (15) |
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16 | (3) |
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19 | (12) |
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1.3 Establishing the Theory |
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31 | (24) |
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31 | (5) |
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1.3.2 Geometrical Approach: Hermite and Minkowski |
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36 | (7) |
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43 | (10) |
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1.3.4 Frobenius and Stickelberger |
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53 | (2) |
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55 | (5) |
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60 | (3) |
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2 The Turn of the Century |
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63 | (32) |
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63 | (10) |
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63 | (2) |
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65 | (6) |
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2.1.3 After the Zahlbericht |
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71 | (2) |
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73 | (12) |
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2.2.1 Field Index and Monogenic Fields |
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73 | (4) |
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77 | (2) |
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79 | (6) |
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2.3 The Beginnings of Class-Field Theory |
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85 | (10) |
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2.3.1 Kronecker's Jugendtraum |
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85 | (3) |
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88 | (3) |
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2.3.3 Hilbert's Class-Field |
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91 | (4) |
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3 First Years of the Century |
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95 | (46) |
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95 | (19) |
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95 | (8) |
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3.1.2 Erich Hecke and the New L-Functions |
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103 | (11) |
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114 | (13) |
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114 | (3) |
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117 | (3) |
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3.2.3 Discriminants and Integral Bases |
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120 | (2) |
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122 | (3) |
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125 | (1) |
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126 | (1) |
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127 | (6) |
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127 | (3) |
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130 | (3) |
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133 | (5) |
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138 | (3) |
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141 | (48) |
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141 | (12) |
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141 | (3) |
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4.1.2 Integral Bases, Discriminants, Factorizations |
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144 | (6) |
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150 | (3) |
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153 | (8) |
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4.2.1 Quadratic Reciprocity Law |
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153 | (2) |
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155 | (2) |
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157 | (1) |
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158 | (1) |
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4.2.5 Values of Zeta-Functions |
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159 | (2) |
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161 | (14) |
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161 | (3) |
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164 | (8) |
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172 | (3) |
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4.4 Class-Number and Class-Group |
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175 | (5) |
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175 | (3) |
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178 | (2) |
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180 | (9) |
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180 | (2) |
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4.5.2 Algebraic Numbers in the Plane |
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182 | (2) |
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4.5.3 Infinite Extensions |
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184 | (1) |
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185 | (1) |
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186 | (3) |
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189 | (40) |
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189 | (8) |
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189 | (1) |
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5.1.2 Integral Bases, Discriminants, Factorizations |
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190 | (4) |
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194 | (3) |
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197 | (8) |
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197 | (5) |
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202 | (3) |
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5.3 Class-Number and Class-Group |
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205 | (7) |
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205 | (6) |
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211 | (1) |
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212 | (17) |
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212 | (2) |
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214 | (1) |
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5.4.3 Euclidean Algorithm |
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215 | (1) |
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5.4.4 Algebraic Numbers on the Plane |
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215 | (7) |
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5.4.5 Infinite Extensions |
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222 | (1) |
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223 | (2) |
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5.4.7 Algebraic Numbers and Matrices |
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225 | (1) |
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226 | (3) |
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229 | (30) |
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229 | (8) |
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229 | (5) |
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234 | (3) |
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237 | (8) |
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6.2.1 Class-Number of Quadratic Fields |
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237 | (5) |
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6.2.2 Class-Number of Cyclotomic Fields |
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242 | (3) |
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245 | (4) |
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249 | (2) |
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251 | (6) |
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257 | (2) |
| Bibliography |
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259 | (158) |
| Author Index |
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417 | (18) |
| Subject Index |
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435 | |
Wladyslaw Narkiewicz is a Polish mathematician who is particularly active in the fields of (analytic) number theory, algebra and the history of mathematics. He received his PhD in 1961 and his habilitation in 1967 at the University of Wroclaw, where he also taught from 1974 to 2006 as a full professor. He is the author of several Springer books, among which the Rational Number Theory in the 20th Century and The Development of Prime Number Theory. Narkiewicz held during his career various administrative functions at the University of Wroclaw, including Deputy Head of the Mathematical Institute, Dean of the Faculty of Mathematics and Physics and Vice Rector for Scientific Affairs. In 1968 he was awarded the Stefan Banach Prize.
