International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 63918, 17 pages
Fourier expansions of complex-valued Eisenstein series on finite
upper half planes
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
Received 11 May 2006; Revised 20 July 2006; Accepted 25 July 2006
Copyright © 2006 Anthony Shaheen and Audrey Terras. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider complex-valued modular forms on finite upper half planes and obtain Fourier expansions of Eisenstein series invariant under the groups
and . The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the -Bessel functions being replaced by Kloosterman sums.