Structures on the Space of Multiplicative Functions

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"A multiplicative function is a function f from the positive integers to the complex numbers such that f(1)=1 and if a and b are coprime integers then f(ab) = f(a) 2020____Thesis completed crossref CSV final merge merge-old.sh merge.sh old posters Release Forms Release.pdf releases T2020-145.xml temp test test.csv test.pdf theses thesis_doi.xml Thesis_Final.pdf thesis-old.xml Thesis.pdf thesis.sh thesis.sh.bak thesis.sh.bak2 thesis-test.sh thesis.xml todo.txt f(b). These functions are of great interest in number theory. Certain multiplicative functions capture important properties of the integers, and other large classes of multiplicative functions have been used to prove notable number-theoretic results. In my thesis, I consider a few of the structures that arise on the space of multiplicative functions and point to some ways that these structures might be useful, particularly in the study of mean values."

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