Yuri Linnik

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.^[1]

• Linnik's theorem in analytic number theory
• The dispersion method (which allowed him to solve the Titchmarsh problem).^[2]
• 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 Linnik (1968), which allowed him to study the distribution properties of the representations of integers by integral ternary quadratic forms.^[3]

Infinitely divisible distributions

Linnik obtained numerous results concerning infinitely divisible distributions.^[4] 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 Linnik & Ostrovskii (1977) 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

• Linnik, Yu.V. (1971), Independent and stationary sequences of random variables, Series of Monographs and Textbooks on Pure and Applied Mathematics, Groningen: Wolters-Noordhoff Publishing
• Linnik, Yu.V. (1961), Method of least squares and principles of the theory of observations, New York-Oxford-London-Paris: Pergamon Press, MR 0124121
• Linnik, Yu.V.; Ostrovskii, I.V. (1977), Decomposition of random variables and vectors, Translations of Mathematical Monographs, vol. 48, Providence, R.I.: American Mathematical Society
• Linnik, Yu.V. (1968), Ergodic properties of algebraic fields, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 45, New York: Springer-Verlag New York Inc.

• Yuri Linnik at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Yuri Linnik", MacTutor History of Mathematics Archive, University of St Andrews
• Acta Arithmetica: Linnik memorial issue (1975)
• List of books by Linnik provided by National Library of Australia