Nikolai Grigoryevich Chebotaryov

Nikolai Chebotaryov ( Russian Николай Григорьевич Чеботарёв , Ukrainian Микола Григорович Чеботарьов ; English transcription Nikolai Chebotaryov; born June 3 ^{. Jul} / 15. June  1894 ^greg. In Kamianets-Podilskyi , † 2. July 1947 in Moscow ) was a Soviet mathematician . He was best known for the Chebotaryov density theorem named after him , a main result of algebraic number theory .

Life

Chebotaryov studied mathematics at the University of Kiev from 1912 to 1918 and then worked as a private teacher and research assistant. In 1921 he moved to Odessa to support his parents living there. During this time, in 1922, Chebotarev found the well-known density theorem, which was to become the basis of his later habilitation (Russian doctoral degree). In 1924 he got the post of Dmitri Fjodorowitsch Jegorow , who had been deposed for political reasons, in Moscow, but resigned a little later and moved back to Odessa. In 1925 he attended a meeting of the German Mathematicians Association in Danzig , where he met Emmy Noether , Helmut Hasse and Kurt Hensel and then visited Berlin ( Issai Schur ) and Göttingen. In 1927 the Ukrainian Academy of Sciences in Kiev awarded him the Russian doctorate. In 1928 he received a professorship at the University of Kazan , which he held until his death. He founded his own school of algebraists there.

His density theorem, published in 1923, generalizes Dirichlet's theorem of prime numbers in arithmetic progressions and solves a problem posed by Ferdinand Georg Frobenius in 1896 . It served Emil Artin in 1927 in the proof of his reciprocity law, a main result of the class field theory .

In later years he dealt with Galois theory , about which he wrote a textbook in two volumes (1934, 1937), and the inverse Galois problem (to find the corresponding equations for a given Galois group). He also dealt with the problem of the resolvent , which goes back to Felix Klein and aims to reduce (by means of a rational transformation) an algebraic equation with parameter-dependent coefficients to an equation whose coefficients depend on as few parameters as possible. Chebotaryov also applied the Galois theory in 1934 to the problem of the constructibility of lunas, which went back to antiquity and was taken up by Leonhard Euler and Thomas Clausen , among others . Chebotaryov also dealt with the theory of Lie groups , in 1940 he published the first Russian textbook on Lie groups, the geometry of translational surfaces and the history of mathematics.

In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (The tasks of modern Galois theory).

Mark Grigoryevich Kerin and Vladimir Vladimirovich Morozov are among his students . In 1929 he became a corresponding member of the Soviet Academy of Sciences. In 1948 he was posthumously awarded the Soviet State Prize for his work on resolvent theory. In 1943 he became an Honored Scientist of the Russian Republic.

Fonts

• Collected works (Russian), 3 volumes, Moscow, Leningrad 1949–1950

The German translation of the original Russian work on the density theorem published in 1923 appeared in the Mathematische Annalen in 1925 :

• N. Tschebotareff: The determination of the density of a set of prime numbers which belong to a given substitution class . In: Mathematischen Annalen 95 (1925), pp. 191-228 ( digitized version ).

Literature and Sources

• P. Stevenhagen, HW Lenstra : Chebotarëv and his Density Theorem . In: The Mathematical Intelligencer 18 (1996), pp. 26-37 ( PDF; 2.7 MB ).
• Adolf Pawlowitsch Juschkewitsch , Article Cheboaryov in Dictionary of Scientific Biography , Online

Web links

• John J. O'Connor, Edmund F. Robertson :  Nikolai Grigorjewitsch Tschebotarjow. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Chebotarev The Problem of Resolvents and Critical Manifolds (Russian), Izvestija Akademia Nauka SSR, Volume 7, 1943, pp. 123–146