Yuri Linnik

Yuri Vladimirovich Linnik (; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics.

Biography

Linnik was born in Bila Tserkva, in present-day Ukraine. He went to Saint Petersburg University where his supervisor was Vladimir Tartakovsky, and later worked at that university and the Steklov Institute. He was a member of the Academy of Sciences of the Soviet Union, as was his father, Vladimir Pavlovich Linnik. He was awarded both Stalin and Lenin Prizes. He died in Leningrad.

Work in number theory

• Linnik's theorem in analytic number theory
• The dispersion method (which allowed him to solve the Titchmarsh problem).
• The large sieve (which turned out to be extremely influential).
• An elementary proof of the Hilbert-Waring theorem; see also Schnirelmann density.
• The Linnik ergodic method, see , which allowed him to study the distribution properties of the representations of integers by integral ternary quadratic forms.

Work in probability theory and statistics

Infinitely divisible distributions

Linnik obtained numerous results concerning infinitely divisible distributions. In particular, he proved the following generalisation of Cramér's theorem: any divisor of a convolution of Gaussian and Poisson random variables is also a convolution of Gaussian and Poisson.

He has also coauthored the book on the arithmetics of infinitely divisible distributions.

Central limit theorem

• Linnik zones (zones of asymptotic normality)
• Information-theoretic proof of the central limit theorem

Statistics

• Behrens–Fisher problem

Selected publications

Notes

External links

• Acta Arithmetica: Linnik memorial issue (1975)
• List of books by Linnik provided by National Library of Australia