I mean to say that an Euler product can be thought of as an iteration of multiplication and so therefore should have fractional iterates correct?

I think such an extension should probably obey, z E C, G is the gamma function, E(...) is an euler product: E( k=0, z ) k = G(z + 1)

I'm curious as to what

E(k=0, z) f(k) =?

Does anyone know where I could find something about this?

I think such an extension should probably obey, z E C, G is the gamma function, E(...) is an euler product: E( k=0, z ) k = G(z + 1)

I'm curious as to what

E(k=0, z) f(k) =?

Does anyone know where I could find something about this?