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The Normal Distribution of ω(φ(m)) in Function Fields
Abstract
Let ω(m) be the number of distinct prime factors of m. A
celebrated theorem of Erdös-Kac states that the quantity
(ω(m)-loglog m)/√(loglog m) distributes
normally. Let φ(m) be Euler's φ-function. Erdös and
Pomerance proved that the
quantity(ω(φ(m)-(1/2)(loglog
m)^2)\((1/√(3)(loglog m)^(3/2)) also distributes
normally. In this thesis, we prove these two results. We also
prove a function field analogue of the Erdös-Pomerance Theorem
in the setting of the Carlitz module.
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Cite this version of the work
Li Li
(2008).
The Normal Distribution of ω(φ(m)) in Function Fields. UWSpace.
http://hdl.handle.net/10012/3567
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