Yuri Linnik

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

Yuri Linnik
Born	Yuri Vladimirovich Linnik (1915-01-08)January 8, 1915 Bila Tserkva, Russian Empire
Died	June 30, 1972(1972-06-30) (aged 57) Leningrad, Soviet Union
Nationality	Russian
Alma mater	Saint Petersburg University Steklov Institute
Scientific career
Fields	Mathematics
Institutions	Saint Petersburg University

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.^[1]

Work in number theory

• 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]

Work in probability theory and statistics

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

Selected publications

• 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.

Notes

1. Faddeyev, D. K.; Lozinsky, S. M.; Malyshev, A. V. (1975), "Yuri V. Linnik (1915–1972): a biographical note", Acta Arith., 27: 1–2, doi:10.4064/aa-27-1-1-2, MR 0421941.
2. Bredikhin, B.M. (2001) [1994], "Density method", Encyclopedia of Mathematics, EMS Press
3. Michel, Ph.; Venkatesh, A. (2006), "Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik", Proceedings of ICM 2006, vol. 2, Zurich: Eur. Math. Soc., pp. 421–457
4. Ibragimov, I. A. (1992), "Yu. V. Linnik. Some of his work from the 1950s", St. Petersburg Math. J., 3 (3): 687–696, MR 1150561.

External links

• 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