Chebotarëv and his density theorem. (English) Zbl 0885.11005

Stevenhagen, P.; Lenstra, H. W. jun.

Math. Intell. 18, No. 2, 26-37 (1996).

The authors sketch the life of N. G. Chebotarëv (1894-1947), most famous for his density theorem in algebraic number theory. Two-thirds of the paper are devoted to Chebotarëv’s mathematics. These include a brief history and explanation of the density theorem and its importance, together with a sketch of a proof of it which does not use class field theory (the historical situation). Also included are two further results of Chebotarëv; one on Vandermonde determinants, which has application to the singularities of gap series, and one dealing with whether a certain class of numbers is constructible.
The paper, both mathematically and historically, is very clearly written. There is a picture of Chebotarëv. One small note: while transliteration is always a problem, and the Mathematical Review Journals’ standard is an appropriate one to follow, it is nevertheless a little strange to see Alexander Ostrowski (who, though Russian, spent his career in German speaking institutions, chiefly Göttingen and Basel) referred to as Ostrovskii.

Reviewer: S.L.Segal (Rochester)

MSC:

11-03	History of number theory
11R45	Density theorems
01A60	History of mathematics in the 20th century
01A70	Biographies, obituaries, personalia, bibliographies

Keywords:

Chebotarev density theorem; constructible numbers; singularities of gap series

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