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
- ^ 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
- ^ "MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE". Retrieved 14 April 2018.
- ^ J.Kubilius Probabilistic methods in the Theory of Numbers at Google Books
- ^ 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
- "Selected publications of Professor Jonas Kubilius". Vilnius University. March 5, 2001. Retrieved 14 April 2018.
- "Biography: Jonas Kubilius". www-history.mcs.st-andrews.ac.uk. Retrieved 14 April 2018.
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
- ^ 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
- ^ "MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE". Retrieved 14 April 2018.
- ^ J.Kubilius Probabilistic methods in the Theory of Numbers at Google Books
- ^ 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
- "Selected publications of Professor Jonas Kubilius". Vilnius University. March 5, 2001. Retrieved 14 April 2018.
- "Biography: Jonas Kubilius". www-history.mcs.st-andrews.ac.uk. Retrieved 14 April 2018.