Yuri Vladimirovich Linnik (; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

and

mathematical statistics Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques that are commonly used in statistics inc ...

Biography

Linnik was born in

Bila Tserkva Bila Tserkva ( ; , ) is a city in central Ukraine. It is situated on the Ros (river), Ros River in the historical region of right-bank Ukraine. It is the largest city in Kyiv Oblast (which does not include the city of Kyiv) and serves as the ...

, in present-day

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

. He went to

Saint Petersburg University Saint Petersburg State University (SPBGU; ) is a public research university in Saint Petersburg, Russia, and one of the oldest and most prestigious universities in Russia. Founded in 1724 by a decree of Peter the Great, the university from the be ...

where his supervisor was Vladimir Tartakovsky, and later worked at that university and the

Steklov Institute Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Ste ...

. He was a member of the

Academy of Sciences of the Soviet Union The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (un ...

, as was his father, Vladimir Pavlovich Linnik. He was awarded both

Stalin Joseph Vissarionovich Stalin (born Dzhugashvili; 5 March 1953) was a Soviet politician and revolutionary who led the Soviet Union from 1924 until Death and state funeral of Joseph Stalin, his death in 1953. He held power as General Secret ...

and

Lenin Prize The Lenin Prize (, ) was one of the most prestigious awards of the Soviet Union for accomplishments relating to science, literature, arts, architecture, and technology. It was originally created on June 23, 1925, and awarded until 1934. During ...

s. He died in

Leningrad Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

Work in number theory

Linnik's theorem Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive ''c'' and ''L'' such that, if we denote p(''a'',''d'') the least prime in the arithmet ...

in analytic number theory * The dispersion method (which allowed him to solve the Titchmarsh problem). * The

large sieve The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein on ...

(which turned out to be extremely influential). * An elementary proof of the Hilbert-Waring theorem; see also

Schnirelmann density In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Russian mathematician Lev Schnirelmann, who was the first to study it.Schnirelmann, L.G. (1930).On the ...

. * The Linnik ergodic method, see , which allowed him to study the distribution properties of the representations of integers by integral ternary

quadratic forms In mathematics, a quadratic form is a polynomial with terms all of degree two (" form" is another name for a homogeneous polynomial). For example, 4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to ...

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 Yuri Vladimirovich Linnik (; 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 S ...

(zones of asymptotic normality) *

Information-theoretic Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through ...

proof of the

central limit theorem In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distributi ...

Statistics

Behrens–Fisher problem In statistics, the Behrens–Fisher problem, named after Walter-Ulrich Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations ...

Selected publications

* * * *

Notes

External links

* *
Acta Arithmetica: Linnik memorial issue (1975)List of books by Linnik provided by National Library of Australia
{{DEFAULTSORT:Linnik, Yuri 1915 births 1972 deaths 20th-century Russian mathematicians People from Bila Tserkva Full Members of the USSR Academy of Sciences Members of the Royal Swedish Academy of Sciences Saint Petersburg State University alumni Heroes of Socialist Labour Recipients of the Stalin Prize Recipients of the Lenin Prize Recipients of the Order of the Badge of Honour Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Mathematical statisticians Number theorists Russian statisticians Soviet mathematicians Russian scientists