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Vinogradov used trigonometric series to attack deep problems in analytic number theory.
Vinogradov studied at St Petersburg. He taught at the State University of Perm from 1918 to 1920 and then returned to St Petersburg. He moved to Moscow to become the first director of the Steklov Institute in 1934, a post he held until his death.
The importance of trigonometric sums in the theory of numbers was first shown by Weyl in 1916. In the 1920's the work of Hardy and Littlewood developed Weyl's methods to attack other problems in analytic number theory. However it was Vinogradov who, in a series of papers in the 1930's, brought the method to its full potential.
His methods reached their height in Some theorems concerning the theory of prime numbers written in 1937. Recent research on the type of problems studied by Vinogradov shows that his methods are still the most powerful to push to yet further results.
Vinogradov made many other contributions, for example to the theory of distribution of power residues, non-residues, indices and primitive roots. He often returned to the topic of his first research paper on the error term in an asymptotic formula discovered by Gauss.
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