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 prime in the arithme ...
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 ...
.
* 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 (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 t ...
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