## The Theory of Algebraic Number FieldsA translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher. |

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### Contents

VIII | 3 |

IX | 4 |

X | 5 |

XI | 9 |

XII | 11 |

XIII | 14 |

XIV | 17 |

XV | 20 |

XCII | 161 |

XCIII | 162 |

XCIV | 163 |

XCV | 167 |

XCVI | 168 |

XCVIII | 169 |

XCIX | 171 |

C | 175 |

XVI | 22 |

XVII | 25 |

XVIII | 28 |

XIX | 30 |

XX | 31 |

XXI | 33 |

XXII | 38 |

XXIII | 41 |

XXIV | 43 |

XXV | 45 |

XXVI | 49 |

XXVII | 51 |

XXVIII | 53 |

XXIX | 56 |

XXXI | 60 |

XXXII | 62 |

XXXIV | 65 |

XXXV | 67 |

XXXVI | 69 |

XXXVII | 72 |

XXXVIII | 73 |

XXXIX | 74 |

XL | 79 |

XLI | 81 |

XLIII | 82 |

XLIV | 83 |

XLV | 84 |

XLVI | 85 |

XLVII | 86 |

XLIX | 87 |

L | 89 |

LI | 90 |

LII | 93 |

LIII | 94 |

LV | 97 |

LVI | 98 |

LVII | 101 |

LVIII | 105 |

LIX | 106 |

LX | 108 |

LXI | 109 |

LXII | 111 |

LXIII | 115 |

LXIV | 116 |

LXV | 118 |

LXVI | 119 |

LXVIII | 121 |

LXIX | 125 |

LXX | 126 |

LXXI | 127 |

LXXIII | 128 |

LXXIV | 131 |

LXXV | 133 |

LXXVI | 135 |

LXXVII | 136 |

LXXX | 138 |

LXXXI | 139 |

LXXXIII | 140 |

LXXXIV | 142 |

LXXXV | 144 |

LXXXVI | 146 |

LXXXVII | 147 |

LXXXVIII | 149 |

LXXXIX | 152 |

XC | 155 |

XCI | 157 |

CI | 176 |

CII | 177 |

CIII | 178 |

CIV | 181 |

CV | 184 |

CVI | 187 |

CVII | 188 |

CIX | 193 |

CX | 194 |

CXI | 195 |

CXIII | 199 |

CXIV | 200 |

CXV | 207 |

CXVI | 208 |

CXVII | 211 |

CXVIII | 213 |

CXIX | 215 |

CXX | 217 |

CXXI | 219 |

CXXII | 220 |

CXXIII | 225 |

CXXIV | 226 |

CXXV | 229 |

CXXVI | 230 |

CXXVII | 233 |

CXXVIII | 243 |

CXXIX | 248 |

CXXX | 253 |

CXXXI | 257 |

CXXXII | 259 |

CXXXIII | 262 |

CXXXIV | 264 |

CXXXV | 265 |

CXXXVI | 266 |

CXXXVII | 269 |

CXXXVIII | 270 |

CXL | 271 |

CXLI | 273 |

CXLII | 280 |

CXLIII | 282 |

CXLIV | 285 |

CXLV | 286 |

CXLVI | 289 |

CXLVII | 290 |

CXLVIII | 293 |

CXLIX | 296 |

CL | 298 |

CLI | 300 |

CLII | 301 |

CLIII | 303 |

CLIV | 305 |

CLV | 306 |

CLVI | 308 |

CLVII | 309 |

CLVIII | 313 |

CLIX | 315 |

CLX | 318 |

CLXI | 321 |

CLXII | 324 |

CLXIII | 325 |

CLXIV | 327 |

CLXV | 332 |

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347 | |

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### References to this book

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### References from web pages

Import Export International

... on the theory of algebraic numbers; Y. Hellegouarch Invitation aux mathematiques de Fermat-Wiles; D. Hilbert, The theory of algebraic number fields. ...

www.fen.bilkent.edu.tr/ ~franz/ books.html

1.Hilbert, The theory of algebraic number fields, 3-540-62779-0

Hilbert,(Adamson translation 1998) The theory of algebraic number fields, 3-540-62779-0, twarda opr., 350pp, cena katalogowa DM 119 - cena konferencyjna DM ...

im0.p.lodz.pl/ konferencje/ krynica99/ OmegaPress.html

Hilbert and the internal logic of mathematics

The theory of algebraic number fields,. Hilbert says:. I have attempted to bypass Kummer's heavy apparatus of calculation in order to abide ...

www.springerlink.com/ index/ K8U3R424K50X0K74.pdf

The Theory of Algebraic Number Fields - Number Theory Journals **...**

The Theory of Algebraic Number Fields - Number Theory & Combinatorics. This book is a translation into English of Hilbert's "Theorie der algebraischen ...

www.springer.com/ math/ numbers/ book/ 978-3-540-62779-1

David Hilbert Books

David Hilbert The Theory of Algebraic Number Fields · HILBERT: The Theory of Algebraic Number Fields. David Hilbert Foundations of Geometry ...

www.kolmogorov.com/ hilbert1.html

Maths Books

The Theory of Algebraic Number Fields, David Hilbert. The Theory of Functions, ec Titchmarsh. The Theory of the Riemann Zeta-Function, ec Titchmarsh; ...

www.ufr-mi.u-bordeaux.fr/ ~kowalski/ math-books.html

David Hilbert libri - I Libri dell'autore: David Hilbert - webster.it

The Theory of Algebraic Number Fields · The Theory of Algebraic Number Fields di David Hilbert - Springer - October 1998. Prezzo: € 113.00 ...

www.webster.it/ vai_libri-author_David+Hilbert-shelf_BUS-David+Hilbert-p_1.html

arxiv:math.NT/0510154 v3 14 Jul 2006

[3] D. Hilbert, The Theory of Algebraic Number Fields (trans. I. Adamson),. Springer-Verlag, Berlin, 1998. [4] E. Kummer,Uber eine besondere Art aus ...

arxiv.org/ pdf/ math.NT/ 0510154.pdf

武汉大学图书馆负责维护

The theory of algebraic number fields / David Hilbert; translated from the German by Iain Adamson; with an introduction from Franz Lemmermeyer an Norbert ...

www.lib.whu.edu.cn/ wjzx/ xstb.htm

i adamson libri - I Libri dell'autore: I Adamson **...**

The Theory of Algebraic Number Fields · The Theory of Algebraic Number Fields di David Hilbert - Springer - October 1998. Prezzo: € 113.00 ...

www.libreriauniversitaria.it/ books-author_i+adamson-i+adamson.htm