Integrals of automorphic Green's functions associated to Heegner divisors

Abstract

In the present paper we find explicit formulas for the degrees of Heegner divisors on arithmetic quotients of the orthogonal group $\Orth(2,p)$ and for the integrals of certain automorphic Green's functions associated with Heegner divisors. The latter quantities are important in the study of the arithmetic degrees of Heegner divisors in the context of Arakelov geometry. In particular, we obtain a different proof and a generalization of results of Kudla relating these quantities to the Fourier coefficients of certain non-holomorphic Eisenstein series of weight $1+p/2$ for the metaplectic group $\Mp_2(\Z)$.