Скачать или смотреть The Natural density of sequences and limiting distribution of arithmetic functions

Course Name: Probabilistic Number Theory
Lecture 4: Natural density of sequences and limiting distribution of arithmetic functions
Course Instructor: Kaneenika Sinha

Abstract: We introduce the notion of density in the set of natural numbers. In particular, the notion of natural density overcomes the limitations of probability measures on the set of natural numbers. The natural density of a sequence of natural numbers can be viewed as a "limit" of probability measures. We also introduce the limiting distribution of arithmetic functions (which is a "limit" of distribution functions of sequences of random variables). Does the framework of probability spaces and distribution functions of random variables extend to density and limiting distribution of arithmetic functions? We start investigating this question by defining a normal order of an arithmetic function.

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