Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO _0(m, 2), I

摘要

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.