Task: Question Answering
Input (English): Context_1 : Nikolai Grigorievich Chebotaryov (often spelled Chebotarov or Chebotarev, Russian: Никола́й Григо́рьевич Чеботарёв , Ukrainian: Микола Григорович Чоботарьов ) (15 June [O.S. 3 June] 1894 – 2 July 1947) was a noted Ukrainian and Soviet mathematician. He is best known for the Chebotaryov density theorem. Context_2 : In mathematics, the Khinchin integral (sometimes spelled Khintchine integral), also known as the Denjoy–Khinchin integral, generalized Denjoy integral or wide Denjoy integral, is one of a number of definitions of the integral of a function. It is a generalization of the Riemann and Lebesgue integrals. It is named after Aleksandr Khinchin and Arnaud Denjoy, but is not to be confused with the (narrow) Denjoy integral. Context_3 : Khinchin's theorem may refer to any of several different results by Aleksandr Khinchin: Context_4 : In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers "x", coefficients "a" of the continued fraction expansion of "x" have a finite geometric mean that is independent of the value of "x" and is known as Khinchin's constant. Context_5 : In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Roman alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick formula_1 complex numbers formula_2, and add them together each multiplied by a random sign formula_3, then the expected value of the sum's modulus, or the modulus it will be closest to on average, will be not too far off from formula_4. Context_6 : Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension "K" of the field formula_1 of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of "K". There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime "p" in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes "p" less than a large integer "N", tends to a certain limit as "N" goes to infinity. It was proven by Nikolai Chebotaryov in his thesis in 1922, published in . Context_7 : In applied mathematics, the Wiener–Khinchin theorem, also known as the Wiener–Khintchine theorem and sometimes as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that the autocorrelation function of a wide-sense-stationary random process has a spectral decomposition given by the power spectrum of that process. Context_8 : Felix Ruvimovich Gantmacher (Russian: Феликс Рувимович Гантмахер ) (23 February 1908 – 16 May 1964) was a Soviet mathematician, professor at Moscow Institute of Physics and Technology, well known for his contributions in mechanics, linear algebra and Lie group theory. In 1925–1926 he participated in seminar guided by Nikolai Chebotaryov in Odessa and wrote his first research paper in 1926. Context_9 : Aleksandr Yakovlevich Khinchin (Russian: Алекса́ндр Я́ковлевич Хи́нчин , French: "Alexandre Khintchine" ; July 19, 1894 – November 18, 1959) was a Soviet mathematician and one of the most significant people in the Soviet school of probability theory. Context_10 : In probability theory, the Palm–Khintchine theorem, the work of Conny Palm and Aleksandr Khinchin, expresses that a large number of not necessarily Poissonian renewal processes combined will have Poissonian properties. fact_1 : Aleksandr Yakovlevich Khinchin (Russian: Алекса́ндр Я́ковлевич Хи́нчин , French: "Alexandre Khintchine" ; July 19, 1894 – November 18, 1959) was a Soviet mathematician and one of the most significant people in the Soviet school of probability theory. fact_2 : Nikolai Grigorievich Chebotaryov (often spelled Chebotarov or Chebotarev, Russian: Никола́й Григо́рьевич Чеботарёв , Ukrainian: Микола Григорович Чоботарьов ) (15 June [O.S. 3 June] 1894 – 2 July 1947) was a noted Ukrainian and Soviet mathematician. Question: Aleksandr Khinchin and Nikolai Chebotaryov were both what?
Output (English): Soviet mathematician