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Theorem

Turan-Kubilius Inequality

Number Theory

The Turan-Kubilius inequality, in probabilistic number theory, bounds the mean-square deviation of an additive complex-valued arithmetic function from its average value, providing a tool for establishing the normal order of such functions. Pal Turan proved a special case in 1934, developing it to simplify the proof of the Hardy-Ramanujan theorem on the normal order of the number of distinct prime divisors of an integer, and Jonas Kubilius generalized the result in 1956 and again in 1964. The inequality remains a standard tool for proving further results in analytic number theory about the typical behavior of additive functions. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Proof Year
1934 2
Proof Year
1956 2
Proof Year
1964 2
Classification
Statement Form
Inequality 1
Connections

Has Statement Form

Inequality, Concepts

In Branch

Number Theory, Branches of Mathematics
Source Turan-Kubilius inequality (Wikipedia)

Proved By

Pál Turán, Mathematicians
Source Turan-Kubilius inequality (Wikipedia)
Sources
1. Turan-Kubilius inequality (Wikipedia)
  • Lead section
    The Turán-Kubilius inequality is a mathematical theorem in probabilistic number theory.
  • In Branch: Number Theory, Lead sentence
    uality is a mathematical theorem in probabilistic number theory.
  • Proved By: Pál Turán, Lead paragraph
    The Turán-Kubilius inequality is a mathematical theorem in probabilistic number theory. It is useful for proving results about the
View the Source
2. Turan-Kubilius inequality (Wikipedia)
The theorem was proved in a special case in 1934 by Pal TuranView the Source
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