The Normal Distribution of ω(φ(m)) in Function Fields

Number Theory;Pure Mathematics

Li, Li

University of Waterloo

关键词: Number Theory;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3567/1/thesis8.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Let ω(m) be the number of distinct prime factors of m.Acelebrated theorem of Erdös-Kac states that the quantity(ω(m)-loglog m)/√(loglog m) distributesnormally.Let φ(m) be Euler;;s φ-function.Erdös andPomerance proved that thequantity(ω(φ(m)-(1/2)(loglogm)^2)((1/√(3)(loglog m)^(3/2)) also distributesnormally.In this thesis, we prove these two results.We alsoprove a function field analogue of the Erdös-Pomerance Theoremin the setting of the Carlitz module.