Please, see in this Wikipedia's article the definition and examples of Pólya class. After I tried work easy questions I was asking myself if
Question. Can you to create an example of an infinite product of functions $E_n(s)$ that belong to (in) the Pólya class, and this infinite product $$\prod_{n=1}^\infty E_n(s)$$ also belongs to the Pólya class?
If is required that you work with the conditions that the factors of you infinite product have no roots on $\Im z>0$ I accept it (I am saying this because I don't understand well the theory, thus if you need this condition you can take it).
This is I would like to know if make sense such example, where does converge your infinite product?
Many thanks.