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

Anthony Shaheen, Audrey Terras
2006 International Journal of Mathematics and Mathematical Sciences  
We consider complex-valued modular forms on finite upper half planesHqand obtain Fourier expansions of Eisenstein series invariant under the groupsΓ=SL(2,Fp)andGL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —theK-Bessel functions being replaced by Kloosterman sums.
doi:10.1155/ijmms/2006/63918 fatcat:zriqf6c36vcnzfbnf4erhfcthu