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.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3567 |
| Date | January 2007 |
| Creators | Li, Li |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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