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From 1944 Linnik was professor of mathematics at Leningrad University. He organised the chair of probability theory there and founded the Leningrad school of statistics.
His main research topics were number theory, probability theory and mathematical statistics. He introduced ergodic methods in number theory in his first work. In a 1941 paper he introduced the large sieve method in number theory. In 1950 he introduced the ideas of probability into number theory and introduced the dispersion method in number theory.
Later Linnik made major contributions to probability with his work on limit theorems and was the first to use powerful techniques from analysis in mathematical statistics.
Linnik was President of the Moscow Mathematical Society for many years. He was honoured by many national mathematical societies and was awarded an honorary degree from Paris.
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