International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 17, Article ID 63918, 17 pages
doi:10.1155/IJMMS/2006/63918
Fourier expansions of complex-valued Eisenstein series on finite upper half planes
Anthony Shaheen1
and Audrey Terras2
1Department of Mathematics, California State University, Los Angeles 90032-8204, CA, USA
2Department of Mathematics, University of California, San Diego, La Jolla 92093-0112, CA, USA
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.