I.M. Vinogradov
| Ivan Matveyevich Vinogradov | |
|---|---|
| Born |
14 September 1891 Milolyub village, Velikiye Luki uyezd, Pskov Governorate, Russian Empire |
| Died | 20 March 1983 (aged 91) Moscow, Soviet Union |
| Nationality | Russian |
| Fields | Mathematics |
| Alma mater | St. Petersburg State University |
| Doctoral advisor | James Victor Uspensky |
| Known for | Analytic number theory |
| Notable awards | Fellow of the Royal Society |
Ivan Matveevich Vinogradov ForMemRS(Russian: Ива́н Матве́евич Виногра́дов; IPA: [ɪˈvan mɐtˈvʲejɪvʲɪtɕ vʲɪnɐˈɡradəf]; 14 September 1891 – 20 March 1983) (not to be confused with Askold Ivanovich Vinogradov of the Bombieri-Vinogradov theorem) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR. He was born in the Velikiye Luki district, Pskov Oblast. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for the five-year period (1941–1946) when the institute was directed by Academician Sergei Sobolev. In 1941 he was awarded the Stalin Prize. In 1951 he became a foreign member of the Polish Academy of Sciences and Letters in Kraków.
In analytic number theory, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sums. In its most basic form, it is used to estimate sums over prime numbers, or Weyl sums. It is a reduction from a complicated sum to a number of smaller sums which are then simplified. The canonical form for prime number sums is
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