Is There a Non-Constant Periodic Function Under Dilation?

[zetafunction]

is it possible to find a function f different from $$f(x)=constant$$

with the property $$f(kx)=f(x)$$ for some real and positive 'k' ?

this is somehow 'dilation periodicity' is the equivalent to the periodic funciton $$f(x+k)=f(x)$$ for some positive 'k' for the traslation group

 

[tiny-tim]

yes

try a substitution ​