Linnik, Iurii

Linnik, Iurii Vladimirovich 

Born Jan. 8 (21), 1915, in Belaia Tserkov’, now in Kiev Oblast; died June 30, 1972, in Leningrad. Soviet mathematician. Academician (1964; corresponding member, 1953) of the Academy of Sciences of the USSR. Hero of Socialist Labor (1969). Son of V. P. Linnik.

Iurii V. Linnik graduated from Leningrad University in 1938. He served in the Soviet Army in 1941–42. In 1940–41 and from 1942 he worked in the Leningrad Division of the V. A. Steklov Institute of Mathematics of the Academy of Sciences of the USSR. Beginning in 1944 he was also a professor at Leningrad University.

Linnik’s studies dealt with number theory, probability theory, and mathematical statistics. In number theory Linnik gave an elementary solution of the Waring problem and proved that every large natural number is the sum of seven cubes of natural numbers. He also established that I. M. Vinogradov’s hypothesis of the least quadratic nonresidue is true for almost all moduli. The large sieve method created by Linnik has found important applications in additive number theory. Linnik also proved that the smallest prime in an arithmetic progression whose difference and first term are relatively prime does not exceed a certain constant power of the difference of the progression. Using the dispersion method he created, Linnik solved the Hardy-Little-wood problem of representing natural numbers as the sum of a prime and two squares, the additive divisor problem, the Titch-marsh divisor problem, and other problems in additive number theory.

Linnik introduced new analytic methods into probability theory and mathematical statistics, which allowed him to solve a number of difficult problems. He was primarily interested in limit theorems for independent random variables and nonhomo-geneous Markov chains, a thorough study of infinitely divisible distributions, the characterization of distributions through the properties of statistics, the theory of testing complex hypotheses, and estimation theory.

A recipient of the State Prize of the USSR (1947) and the Lenin Prize (1970), Linnik was awarded the Order of Lenin, the Order of the Badge of Honor, and various medals.

WORKS

Dispersionnyi metod v binarnykh additivnykh zadachakh. Leningrad, 1961.
Metod naimen’shikh kvadratov . . ., 2nd ed. Moscow, 1962.
Elementarnye metody v analiticheskoi teorii chisel. Moscow, 1962. (With A. O. Gel’fond.)
Nezavisimye i statsionarno sviazannye velichiny. Moscow, 1965. (With I. A. Ibragimov.)
Statisticheskie zadachi s meshaiushchimi parametrami. Moscow, 1966.

REFERENCES

“Iurii Vladimirovich Linnik.” Uspekhi matematicheskikh nauk, 1965, vol. 20, issue 2.
Ibid., 1973, vol. 28, issue 2. (Contains a list of works by Linnik.)

A. A. KARATSUBA and IU. V. PROKHOROV