The quantum analog of zeta-function and spector of masses for the alternating zeta-function field theory

In the present work we consider the quantum analogue of Riemann’s zeta-function and its alternating version. Formulas for representation of zeta-functions in the form of a functional series and values in the negative integral points are given. For classical limit are obtained known results. We consider field theory for kinetic term with quantum alternating zeta-function and discuss mass spectrum here.