The value distribution of additive arithmetic functions on a line

2010 ◽  
Vol 2010 (642) ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Value Distribution ◽  
Arithmetic Functions ◽  
Additive Arithmetic

Additive arithmetic functions on intervals

1988 ◽  
Vol 103 (1) ◽  
pp. 163-179 ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Arithmetic Function ◽  
Value Distribution ◽  
Arithmetic Functions ◽  
Additive Arithmetic ◽  
Positive Integers

§1. A real-valued arithmetic function f is additive if it satisfies the relation f(ab) = f(a) + f(b) for all mutually prime positive integers a, b. In the present paper I establish three theorems concerning the value distribution of such functions on intervals.

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