Metamaterials and Ces\`aro convergence

In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Ces`{a}ro convergence. Then, we also show that the analytical continuation of the linear permittivity & permeability to a complex plane in terms of Riemann zeta function. The metamaterials are fabricated materials with a negative refractive index. These materials, in turn, depend on permittivity & permeability of the linear dielectrics and magnetic materials. Therefore, the Ces`{a}ro convergence property of the linear dielectrics and magnetic materials may be used to fabricate the metamaterials.