Yuri Linnik

{{Infobox scientist | honorific_prefix = | name = Yuri Linnik | honorific_suffix = | native_name = | native_name_lang = | image = Yuri Linnik (photo).jpg | image_size = | image_upright = | alt = | birth_name = Yuri Vladimirovich Linnik | birth_date = {{birth date|1915|01|8}} | birth_place = Bila Tserkva, Russian Empire | death_date = {{death date and age|1972|06|30|1915|01|8}} | death_place = Leningrad, Soviet Union | death_cause = | resting_place = | resting_place_coordinates =  | other_names = | siglum = | pronounce = | citizenship =  | fields = Mathematics | workplaces = Saint Petersburg University | patrons = | education = | alma_mater = Saint Petersburg University<br>Steklov Institute | thesis_title =  | thesis_url =  | thesis_year =  | doctoral_advisor =  | academic_advisors = | doctoral_students = | notable_students = | known_for = | influences = | influenced = | awards = | author_abbrev_bot = | author_abbrev_zoo = | spouse =  | partner =  | children = | parents = | father = | mother = | relatives = | signature =  | signature_alt = | website =  | footnotes = }} '''Yuri Vladimirovich Linnik''' ({{langx|ru|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.<ref>{{Citation|mr=0421941|last1=Faddeyev|first1=D. K.|last2=Lozinsky|first2=S. M.|last3=Malyshev|first3=A. V.|title=Yuri V. Linnik (1915–1972): a biographical note|journal=Acta Arith.|volume=27|year=1975|pages=1–2|postscript=.|doi=10.4064/aa-27-1-1-2|doi-access=free}}</ref>

==Work in number theory==

* Linnik's theorem in analytic number theory * The dispersion method (which allowed him to solve the Titchmarsh problem).<ref>{{eom|id=D/d033370|first=B.M.|last=Bredikhin|title=Density method}}</ref> * 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 {{harvtxt|Linnik|1968}}, which allowed him to study the distribution properties of the representations of integers by integral ternary quadratic forms.<ref>{{Citation|last=Michel|first=Ph.|first2=A.|last2=Venkatesh|chapter= Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik|title=Proceedings of ICM 2006|volume=2|publisher=Eur. Math. Soc.|location=Zurich|year=2006|pages=421–457}}</ref>

==Work in probability theory and statistics==

===Infinitely divisible distributions===

Linnik obtained numerous results concerning infinitely divisible distributions.<ref>{{Citation|mr=1150561|last=Ibragimov|first=I. A.|title=Yu. V. Linnik. Some of his work from the 1950s|journal=St. Petersburg Math. J.|volume=3|year=1992|issue=3|pages=687–696|postscript=.}}</ref> 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 {{harvtxt|Linnik|Ostrovskii|1977}} on the arithmetics of infinitely divisible distributions.

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

===Statistics=== * Behrens–Fisher problem

==Selected publications== * {{citation|first=Yu.V.|last=Linnik|title=Independent and stationary sequences of random variables|series=Series of Monographs and Textbooks on Pure and Applied Mathematics|publisher=Wolters-Noordhoff Publishing|location=Groningen|year=1971}} * {{citation|first=Yu.V.|last=Linnik|title=Method of least squares and principles of the theory of observations |mr=0124121|publisher=Pergamon Press|location=New York-Oxford-London-Paris|year=1961}} * {{citation|first=Yu.V.|last=Linnik|first2=I.V.|last2=Ostrovskii|title=Decomposition of random variables and vectors|series=Translations of Mathematical Monographs|volume=48|publisher=American Mathematical Society|location=Providence, R.I.|year=1977}} * {{citation|first=Yu.V.|last=Linnik|title=Ergodic properties of algebraic fields|series=Ergebnisse der Mathematik und ihrer Grenzgebiete|volume=45|publisher=Springer-Verlag New York Inc.|location=New York|year=1968}}

==Notes==

==External links== *{{MathGenealogy |id=44401}} *{{MacTutor Biography|id=Linnik}} *[http://matwbn.icm.edu.pl/tresc.php?wyd=6&tom=27 Acta Arithmetica: Linnik memorial issue (1975)] *[http://nla.gov.au/nla.party-1244588 List of books by Linnik provided by National Library of Australia]

{{DEFAULTSORT:Linnik, Yuri}} Category:1915 births Category:1972 deaths Category:20th-century Russian mathematicians Category:People from Bila Tserkva Category:Full Members of the USSR Academy of Sciences Category:Members of the Royal Swedish Academy of Sciences Category:Saint Petersburg State University alumni Category:Heroes of Socialist Labour Category:Recipients of the Stalin Prize Category:Recipients of the Lenin Prize Category:Recipients of the Order of the Badge of Honour Category:Recipients of the Order of Lenin Category:Recipients of the Order of the Red Banner of Labour Category:Mathematical statisticians Category:Number theorists Category:Russian statisticians Category:Soviet mathematicians Category:20th-century Russian scientists Category:20th-century statisticians