-schemes and toric varieties.
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.
For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.
Page 1