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 ​