Yuri Vladimirovich Linnik (russian: Ю́рий Влади́мирович Ли́нник; January 8, 1915 – June 30, 1972) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

active in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

probability theory Probability theory 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 expressing it through a set o ...

and

mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...

. Linnik was born in

Bila Tserkva Bila Tserkva ( uk, Бі́ла Це́рква ; ) is a city in the center of Ukraine, the largest city in Kyiv Oblast (after Kyiv, which is the administrative center, but not part of the oblast), and part of the Right Bank. It serves as the admi ...

, in present-day

Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inv ...

. He went to

St Petersburg University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...

where his supervisor was Vladimir Tartakovski, and later worked at that university and the Steklov Institute. He was a member of the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...

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

State State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States * ''Our S ...

and Lenin Prizes. He died in

Leningrad Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

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 primes in arithmetic pr ...

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 only ...

(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 a ...

. * 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 a ...

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

(zones of asymptotic normality) *

Information-theoretic Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. T ...

proof of the

central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselv ...

Statistics

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

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 Soviet mathematicians Number theorists Full Members of the USSR Academy of Sciences Heroes of Socialist Labour Russian statisticians Members of the Royal Swedish Academy of Sciences