Dirichlet series of the second kind for irreducible lattices repeated by multiplication

The work constructs a theory of Dirichlet series of the second kind for irreducible lattices repeated by multiplication. In particular, the theorem is proven that Dirichlet series of the second kind for irreducible lattices repeated by multiplication form an algebra over the field of complex numbers.
In conclusion, current problems for Dirichlet series of the second kind for irreducible lattices repeated by multiplication are considered, requiring further research.