Yuri Linnik

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

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.

Biography[edit]

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[edit]

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[edit]

Infinitely divisible distributions[edit]

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[edit]

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

Statistics[edit]

Behrens–Fisher problem

Selected publications[edit]

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[edit]

^ 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.
^ Bredikhin, B.M. (2001) [1994], "Density method", Encyclopedia of Mathematics, EMS Press
^ 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
^ 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[edit]

[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.

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