In the critical dimension d = 26 the p-loop scattering amplitude for tachyons with momenta kα in the bosonic string theory can be expressed through a finite-fold integral over the space Mp of moduli of Riemann surfaces of genus p: ∫DgabDxμ exp(-1/2M2∫d2ξ√ggab∂axμ∂bxμ)αΠ∫d2ξα√g(ξα) exp[ikαx(ξα)] ~ Mp∫ dνp(det N0/det' ∆0)13 det' ∆-1(αΠ∫d2ξα α,βΠ exp[-(1/2M2) kαkβG(ξα, ξβ)]). In the r.h.s. of this formula the two-dimensional metric is supposed to have the conformal form gab = ϱ(ξ) δab ∆j = -ϱj-1∂ϱ-j∂ stands for the Laplace operator ∂+∂ acting on j-differentials f(ξ, ξ) dξj Nj are scalar product matrices of zero modes of the operators i.e. of holomorphic j-differentials: det Nj --- det(mn)∫ƒ;m(ξ) dξj ƒ;n(ξ) dξj/[ϱ(ξ, |ϱ) dξ dξ] j-1 = det(mn)∫ϱ1-jƒ;mƒ;nd2ξ. The functional determinant det' ∆0 comes from integration over the fields xμ (two-dimensional scalars), while det'. ∆-1 is the Faddeev-Popov determinant arising due to fixation of the conformal gauge for gab (the parameters of general coordinate transformations are vectors, i.e. j = -1 differentials). Through GR the regularized Green function on the Riemann surface is denoted.