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Yuri Linnik

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Soviet mathematician (1915–1972)
Yuri Linnik
BornYuri Vladimirovich Linnik
(1915-01-08)January 8, 1915
Bila Tserkva, Russian Empire
DiedJune 30, 1972(1972-06-30) (aged 57)
Leningrad, Soviet Union
NationalityRussian
Alma materSaint Petersburg University
Steklov Institute
Scientific career
FieldsMathematics
InstitutionsSaint 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

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

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 Linnik & Ostrovskii (1977) on the arithmetics of infinitely divisible distributions.

Central limit theorem

Statistics

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) , "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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