Kubilius model

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In mathematics, the Kubilius model relies on a clarification and extension of a finite probability space on which the behaviour of additive arithmetic functions can be modeled by sum of independent random variables. [1]

The method was introduced in Jonas Kubilius's monograph Tikimybiniai metodai skaičių teorijoje (published in Lithuanian in 1959) [2] / Probabilistic Methods in the Theory of Numbers (published in English in 1964) . [3]

Eugenijus Manstavičius and Fritz Schweiger wrote about Kubilius's work in 1992, "the most impressive work has been done on the statistical theory of arithmetic functions which almost created a new research area called Probabilistic Number Theory. A monograph (Probabilistic Methods in the Theory of Numbers) devoted to this topic was translated into English in 1964 and became very influential." [4] :xi

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References

  1. Schwarz, W. (1994). "Some aspects of the development of probabilistic number theory". In Grigelionis, B.; Kubilius, J.; Pragarauskas, H.; Statulevičius, V. (eds.). Probability theory and mathematical statistics: Proceedings of the 6th International Conference held in Vilnius, June 28–July 3, 1993. Vilnius: TEV. pp. 661–701. MR   1649606.; see p. 674
  2. "MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE" . Retrieved 14 April 2018.
  3. J.Kubilius Probabilistic methods in the Theory of Numbers at Google Books
  4. Manstavičius, Eugenijus; Schweiger, Fritz, eds. (1992). Analytic and probabilistic methods in number theory. New Trends in Probability and Statistics. Vol. 2. Utrecht: VSP. ISBN   978-90-6764-094-7 . Retrieved 2009-04-17.

Further reading