Ivan Matveyevich Vinogradov

Ivan Matveyitch Vinogradov (Russian: Иван Матвеевич Виноградов; * 2 Septemberjul / September 14 1891greg in Miloljub, in Ujesd Welikije Luki, Pskov province, .. † March 20, 1983 in Moscow) was a Russian mathematician, considered one of the founders of modern analytic number theory applies.

Life and work

Vinogradov was the son of a priest. He grew up in Welikije Luki and studied from 1910 at the University of St Petersburg, among others, Andrei Markov and James Victor Uspensky. In 1915 he received his degree. His work on the distribution of quadratic residues gave him a scholarship to a PhD. In 1918 he was a lecturer at the newly founded University of Perm, where he became professor in 1919. In 1920 he became a professor at the Polytechnic Institute in Saint Petersburg and at the same time a lecturer at the university. In 1925 he became a professor and head of department of probability theory and number theory. In 1934 he became the director of the newly founded Steklov Institute of Mathematics in Leningrad, at the foundation, he was heavily involved. After moving the Institute to Moscow, it has since been led by Sergei Sobolev Lvovitch, but in 1947 took over Vinogradov again the line, which he held until his death.

Vinogradov developed a method for the evaluation of trigonometric sums of the form

Where the sum extends over all primes below a barrier and is a real number. Such sums first investigated Hermann Weyl, 1916 in analytic number theory, and they were by Godfrey Harold Hardy and John Edensor Littlewood become a powerful tool in number theory expanded (Circle Method, circle method ). 1937 attracted Vinogradov stir when he could prove with his methods that almost all (more precisely all sufficiently large ) odd numbers sum of three primes ( set of Vinogradov ), and thus an important advance in the ( weak or ternary ) could make gold Bach's conjecture. Vinogradov turned his method also to other problems of additive number theory such as the Waring problem.

Vinogradov was twice Hero of the Soviet Union and was awarded the Lomonosov Gold Medal. In 1942 he became a member of the Royal Society. In 1966, he held ( with AG Postnikov ) a plenary lecture at the International Congress of Mathematicians in Moscow ( Recent developments in analytic number theory).

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

Works

  • Selected Works. Berlin, New York, Springer -Verlag, 1985, ISBN 0-387-12788-7
  • Vinogradov, I.M.: Elements of Number Theory. Mineola, NY: Dover Publications, 2003, ISBN 0-486-49530-2
  • Vinogradov, IM: Method of Trigonometrical Sums in the Theory of Numbers. Mineola, NY: Dover Publications, 2004, ISBN 0-486-43878-3
  • Vinogradov, I.M. ( Ed. ): Matematicheskaya entsiklopediya. Moscow, Sov. Entsiklopediya, 1977. Meanwhile, translated into English and expanded as the Encyclopaedia of Mathematics.
Uyezd Pskov Governorate Andrey Markov J. V. Uspensky G. H. Hardy Trigonometric polynomial Vinogradov's theorem Encyclopedia of Mathematics Integrated Authority File
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