scholarly journals Weakly multiplicative arithmetic functions and the normal growth of groups

2018 ◽  
Vol 112 (3) ◽  
pp. 233-240
Author(s):  
Jan-Christoph Schlage-Puchta
Keyword(s):  
Normal Growth ◽  
Arithmetic Functions ◽  
Growth Of Groups ◽  
Multiplicative Arithmetic

Additive and multiplicative functions from Nottingham to Urbana-Champaign

2015 ◽  
Vol 11 (05) ◽  
pp. 1357-1366
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Arithmetic Functions ◽  
Multiplicative Functions ◽  
Joint Work ◽  
Multiplicative Arithmetic

The author remembers Heini Halberstam and views their early joint work through the lens of additive and multiplicative arithmetic functions.

scholarly journals Completely multiplicative functions arising from simple operations

2004 ◽  
Vol 2004 (9) ◽  
pp. 431-441
Author(s):  
Vichian Laohakosol ◽  
Nittiya Pabhapote
Keyword(s):  
Arithmetic Functions ◽  
Multiplicative Functions ◽  
Convolution Powers ◽  
Multiplicative Arithmetic

Given two multiplicative arithmetic functions, various conditions for their convolution, powers, and logarithms to be completely multiplicative, based on values at the primes, are derived together with their applications.

scholarly journals On a subgroup of the group of multiplicative arithmetic functions

1975 ◽  
Vol 20 (3) ◽  
pp. 348-358 ◽  
Author(s):  
T. B. Carroll ◽  
A. A. Gioia
Keyword(s):  
Abelian Group ◽  
Arithmetic Function ◽  
Arithmetic Functions ◽  
Greatest Common Divisor ◽  
Multiplicative Functions ◽  
Dirichlet Convolution ◽  
Image Position ◽  
Positive Integers ◽  
Multiplicative Arithmetic

An arithmetic function f is said to be multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1, where (m, n) denotes as usual the greatest common divisor of m and n. Furthermore an arithmetic function is said to be linear (or completely multiplicative) if f(1) = 1 and f(mn) = f(m)f(n) for all positive integers m and n.The Dirichlet convolution of two arithmetic functions f and g is defined by for all n∈Z+. Recall that the set of all multiplicative functions, denoted by M, with this operation is an abelian group.

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