Integral limit theorems for sums of additive functions with shifted arguments

1995 ◽  
Vol 59 (2) ◽  
pp. 401-426
Author(s):  
N M Timofeev
Keyword(s):  
Limit Theorems ◽  
Additive Functions ◽  
Integral Limit

Some integral limit theorems for additive functions

1977 ◽  
Vol 16 (4) ◽  
pp. 564-573
Author(s):  
B. V. Levin ◽  
N. M. Timofeev
Keyword(s):  
Limit Theorems ◽  
Additive Functions ◽  
Integral Limit

Integral Limit Laws for Additive Functions

1973 ◽  
Vol 25 (1) ◽  
pp. 194-203
Author(s):  
J. Galambos
Keyword(s):  
Characteristic Function ◽  
Fourier Transforms ◽  
Mean Value ◽  
Characteristic Functions ◽  
Asymptotic Formulas ◽  
Mean Value Theorem ◽  
Multiplicative Functions ◽  
Additive Functions ◽  
Limit Laws ◽  
Integral Limit

In the present paper a general form of integral limit laws for additive functions is obtained. Our limit law contains Kubilius’ results [5] on his class H. In the proof we make use of characteristic functions (Fourier transforms), which reduces our problem to finding asymptotic formulas for sums of multiplicative functions. This requires an extension of previous results in order to enable us to take into consideration the parameter of the characteristic function in question. We call this extension a parametric mean value theorem for multiplicative functions and its proof is analytic on the line of [4].

Sign in / Sign up

Export Citation Format

Share Document