The theory of algebraic number fields. Transl. from the German by Iain T. Adamson. With an introduction by Franz Lemmermeyer and Norbert Schappacher. (English) Zbl 0984.11001

Hilbert, David

Berlin: Springer. xxxvi, 350 p. (1998).

This is the first English translation (made by I. T. Adamson) of the famous Zahlbericht of David Hilbert [Jahresber. DMV 4, i-xviii, 175-546 (1897; JFM 28.0157.05)]. The German original has been reprinted in Hilbert’s “Gesammelte Abhandlungen”, Springer (1932; Zbl 0004.09801; repr. 1970; Zbl 0195.00401), which contained an exposition of the theory of algebraic number fields and had a great influence on the development of that subject in the 20th century. An introduction written by F. Lemmermeyer and N. Schappacher describes certain aspects of Hilbert’s treatise from a modern point of view.

Reviewer: Władysław Narkiewicz (Wrocław)

MSC:

11-02	Research exposition (monographs, survey articles) pertaining to number theory
11-03	History of number theory
01A75	Collected or selected works; reprintings or translations of classics
11Rxx	Algebraic number theory: global fields
01A55	History of mathematics in the 19th century
11D41	Higher degree equations; Fermat’s equation

Keywords:

algebraic numbers; algebraic number fields; JFM 28.0157.05

Citations:

Zbl 0004.09801; Zbl 0195.00401; JFM 28.0157.05