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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-07-23 and was most recently seen on 2026-07-23.
In number theory, a real-valued function on the integers is additive if for coprime m, n. The Erdős–Wintner theorem gives a condition under which a real-valued additive function has a limiting distribution
In particular, it asserts that the limiting function exists if the three following series pertaining to prime numbers converge:
When this happens, the characteristic function of the limiting distribution is equal to
where is the imaginary unit. Furthermore, the limiting distribution is continuous if and only if the series
diverges, otherwise the distribution is purely discrete.
It is an analogue in probabilistic number theory of Kolmogorov's three-series theorem.
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