On Local Theorems for Additive Number-Theoretic Functions

J. Kubilius

A chapter in Number Theory and Analysis, 1969, pp 173-191 from Springer

Abstract: Abstract In the present paper the distribution of values of additive number-theoretic functions is considered. A function f(m) defined for all positive integers m = 1, 2, … is called additive if f(mn) = f(m) + f(n) provided (m, n) = 1. The theory of integral limit laws for these functions has been developed by many authors. As to local laws which are generally speaking deeper very little is known. In this case it is a matter of finding an asymptotic expression for the number N n (a) of positive integers m ≦ n for which f(m) assumes a given value a. Theorems of such kind are the asymptotic law of prime numbers as well as the asymptotic laws of positive integers having a given number of prime divisors.

Keywords: Positive Integer; Additive Function; Prime Divisor; Dirichlet Series; Multiplicative Function (search for similar items in EconPapers)
Date: 1969
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-4819-5_12

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DOI: 10.1007/978-1-4615-4819-5_12

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