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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.

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

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."

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

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