Ivan Matveevich Vinogradov

Grave bust of Vinogradov in the Novodevichy Cemetery

Ivan Matveyevich Vinogradov ( Russian Иван Матвеевич Виноградов ; born September 2nd ^{. Jul} / 14. September  1891 ^greg. In Miloljub, in Ujesd Velikiye Luki , Pskov Governorate ; † 20th March 1983 in Moscow ) was a Soviet mathematician who was one Co-founder of modern analytical number theory applies.

life and work

Vinogradov was the son of a priest . He grew up in Velikije Luki and studied from 1910 at the University of Saint Petersburg with Andrei Markov and James Victor Uspensky, among others . In 1915 he graduated. His work on the distribution of square scraps earned him a scholarship to do a doctorate. In 1918 he was a lecturer at the newly established Perm University , where he became a professor in 1919. In 1920 he became professor at the Polytechnic Institute in Saint Petersburg and at the same time lecturer at the university. In 1925 he became professor and head of the department for probability theory and number theory. In 1934 he became the head of the newly founded Steklov Institute for Mathematics in Leningrad, in the establishment of which he played a key role. After the institute moved to Moscow, it was temporarily headed by Sergei Lwowitsch Sobolew , but from 1947 Vinogradov took over the management again, which he held until his death.

Winogradow developed a method for evaluating trigonometric sums of shape

${\displaystyle f(\alpha ,N)=\sum _{p\leq N}\exp {(2\pi i\alpha p)}}$,

where the sum extends over all prime numbers below a bound and is a real number. Such sums first explored Hermann Weyl in 1916 in analytic number theory, and they were of Godfrey Harold Hardy and John Edensor Littlewood developed into a powerful tool in number theory ( Circle Method , circle method ). 1937 attracted Vinogradov stir when he proved with his methods that almost all (more precisely all sufficiently large) odd numbers are the sum of three primes ( Vinogradov's theorem ) and thus an important advance in the (weak or ternary) Gold Bach's guess making could . Winogradov also applied his method to other problems of additive number theory such as the Waring problem . ${\displaystyle p}$ ${\displaystyle N}$ ${\displaystyle \alpha }$

Vinogradov played an inglorious role in the implementation of anti-Semitic activities in the Soviet scientific community ( Lev Pontryagin was also important ) and operated the release of Jewish employees at the Steklov Institute in Leningrad almost as a personal crusade .

Vinogradov received the Stalin Prize (1941), the Lenin Prize (1972) and the State Prize of the USSR (1983). He was twice Hero of the Soviet Union (1945, 1971) and received the Lomonosov Gold Medal (1970). In 1942 he became a member of the Royal Society and the American Philosophical Society . In 1962 he was elected a member of the Leopoldina . Since 1946 he was a corresponding member of the Académie des sciences .

In 1966 he gave (with AG Postnikov) a plenary lecture at the International Congress of Mathematicians in Moscow ( Recent Developments in Analytical Number Theory ).

He should not be confused with the number theorist Askold Ivanovich Vinogradov (from the Bombieri- Vinogradov theorem).

Works

• Elements of number theory (= university books for mathematics . Vol. 22). German Science Publishing House, Berlin 1955.
• (Ed.): Matematicheskaya entsiklopediya. Moscow 1977 (translated into English and expanded as Encyclopaedia of Mathematics ).
• Selected Works. Berlin, New York, Springer-Verlag, 1985, ISBN 0-387-12788-7
• Method of Trigonometrical Sums in the Theory of Numbers. Dover Publications, Mineola, NY 2004, ISBN 0-486-43878-3 .

Web links

• John J. O'Connor, Edmund F. Robertson :  Iwan Matwejewitsch Winogradow. In: MacTutor History of Mathematics archive .
• Literature by and about Iwan Matwejewitsch Winogradow in the catalog of the German National Library
• Article Ivan Matwejewitsch Vinogradow in the Great Soviet Encyclopedia (BSE) , 3rd edition 1969–1978 (Russian)http: //vorlage_gse.test/1%3D005176~2a%3D~2b%3DIwan%20Matwejewitsch%20Winogradow

References

1. ↑ Winogradow, Doklady Akad. Nauk SSR, Vol. 15, 1937, pp. 291-294
2. ↑ In 1923 Hardy and Littlewood proved this statement with their circle method, assuming the generalized Riemann hypothesis . Winogradov proved this without any preconditions using the circle method and his method of estimating trigonometric sums.
3. ↑ Masha Gessen, Perfect Rigor , Houghton Mifflin Harcourt, 2009, p. 103
4. ^ Biography of Vinogradov on the website of the Russian Academy of Sciences. Retrieved June 2, 2020 . 
5. ↑ Member History: Ivan M. Vinogradov. American Philosophical Society, accessed November 14, 2018 . 
6. ↑ Member entry of Ivan M. Vinogradov at the German Academy of Natural Scientists Leopoldina , accessed on June 12, 2016.
7. ^ List of former members since 1666: Letter V. Académie des sciences, accessed on March 12, 2020 (French).