Georgian Mathematical Journal 13 (2006), No. 1, 055--078
Copyright Heldermann Verlag 2006
On the Fourier Expansions of Eisenstein Series of Some Types
Nikoloz Kachakhidze
Dept. of Mathematics No. 3, Georgian Technical University, 77 M. Kostava St., Tbilisi 0193, Georgia
nika3966@yahoo.com
[Abstract-pdf]
Bases of the spaces of Eisenstein series $E_k(\Gamma_0(4N),\chi)$ $(k\in \mathbb{N}$, $k\geq 3$, $N$ is an odd natural and square-free) and $E_{k/2}(\widetilde\Gamma_0(4N),\chi)$ $(k\in \mathbb{N}$, $k$ impair, $k\geq 5$, $N$ is an odd natural and square-free) are constructed for any Dirichlet character mod $4N$ and Fourier expansions of these series are obtained.
Keywords: Entire modular form, Eisenstein series, congruence subgroup.
MSC: 11F11
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