Yuri Linnik
Yuri Vladimirovich Linnik 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.
- The large sieve.
- 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
- Information-theoretic proof of the central limit theorem
Statistics
- Behrens–Fisher problem
Selected publications