Studies in multiplicative number theory
Publication Date
1980
Creator
Abstract
This thesis gives some order estimates and asymptotic formulae associated with general classes of non-negative multiplicative functions as well as some particular multiplicative functions such as the divisor functions dk(n).
In Chapter One we give a lower estimate for the number of distinct values assumed by the divisor function d(n) in 1 or = 1
then the maximum value of f(n) in 1 infinity.
We call a positive integer n a k-full integer if pk divides n whenever p is a prime divisor of n, and in Chapter Four we give an asymptotic formula for the number of k-full integers not exceeding x. In Chapter Five we give an asymptotic formula for the number of 2-full integers in an interval. We also study the problem of the distribution of the perfect squares among the sequence of 2-full integers.
The materials in the first three chapters have been accepted for publications and will appear [31], [22], [33] and [32].
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
28304
UoN Repository URI
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