Algebraicity of higher Green functions at a CM point

Abstract In this paper, we investigate the algebraic nature of value a higher Green function on an orthogonal Shimura variety at single CM point. This is motivated by conjecture Gross and Zagier in setting functions product two modular curves. process, will study analogue harmonic Maass forms Hilbert forms, obtain results concerning arithmetic their holomorphic part Fourier coefficients. As consequence, answer question his 1986 ICM proceeding.