Kubilius_model

Kubilius model

Kubilius model

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See also: Probabilistic number theory

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 

References

  1. [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. [2]
    "MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE". Retrieved 14 April 2018.
  3. [3]
    J.Kubilius Probabilistic methods in the Theory of Numbers at Google Books
  4. [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.

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