Fourier expansions of complex-valued Eisenstein series on finite upper half planes

Abstract

We consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K-Bessel functions being replaced by Kloosterman sums.