Metamaterials and Ces\`aro convergence
Abstract
In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Ces\`aro 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\`aro convergence property of the linear dielectrics and magnetic materials may be used to fabricate the metamaterials.
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