multiplicative arithmetic function
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2015 ◽  
Vol 11 (06) ◽  
pp. 1905-1912 ◽  
Author(s):  
Colin Defant

For a real number t, let st be the multiplicative arithmetic function defined by [Formula: see text] for all primes p and positive integers α. We show that the range of a function s-r is dense in the interval (0, 1] whenever r ∈ (0, 1]. We then find a constant ηA ≈ 1.9011618 and show that if r > 1, then the range of the function s-r is a dense subset of the interval [Formula: see text] if and only if r ≤ ηA. We end with an open problem.


1965 ◽  
Vol 5 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Jack P. Tull

Let α(n) be a multiplicative arithmetic function. H. Delange [1] has proved that if |α(n)| ≦ 1 for all n and for a certain constant ρ, , where if ρ = 1 then then . He applied this result to several problems such as uniform distribution (mod 1) of certain types of sequences.


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