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

Shaheen, Anthony; Terras, Audrey

doi:https://doi.org/10.1155/IJMMS/2006/63918

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 063918 | https://doi.org/10.1155/IJMMS/2006/63918

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

Anthony Shaheen¹and Audrey Terras²

Received11 May 2006

Revised20 Jul 2006

Accepted25 Jul 2006

Published01 Nov 2006

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.

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Copyright © 2006 Hindawi Publishing Corporation. 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.

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