Probabilistic number theory

Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions of number theory. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables. This however is not an idea that has a unique useful formal expression.

The founders of the theory were Paul Erdős, Aurel Wintner and Mark Kac during the 1930s, one of the periods of investigation in analytic number theory. The Erdős–Wintner theorem and the Erdős–Kac theorem on additive functions were foundational results.

See also

• analytic number theory
• areas of mathematics
• list of number theory topics
• list of probability topics
• mathematics
• probabilistic method
• probable prime

References

• Tenenbaum, Gérald (1995). Introduction to Analytic and Probabilistic Number Theory. Cambridge studies in advanced mathematics. Vol. 46. Cambridge University Press. ISBN 0-521-41261-7. Zbl 0831.11001.

Further reading

• Kubilius, J. (1964) [1962]. Probabilistic methods in the theory of numbers. Translations of mathematical monographs. Vol. 11. Providence, RI: American Mathematical Society. ISBN 0-8218-1561-X. Zbl 0133.30203.