Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO0(m,2), I

Given a maximal even integral lattice L of signature (m+,2−) (m≥3), we consider an orthonormal Hecke eigen basis Bl of the holomorphic cusp forms of weight l on a tube domain with respect to the discriminant subgroup of the orthogonal group O(L). We construct a certain adèlic holomorphic Poincaré series whose spectral expansion is described by the central standard L-value of F∈Bl and the square of a Fourier–Bessel coefficient of F.