Nikoloz Kachakhidze

On the Fourier Expansions of Eisenstein Series of Some Types

Abstract:
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 $E_{k/2}(\wt\Gamma_0(4N),\chi)$ $(k\in \mathbb{N}$, $2\dag k$, $k\geq 5$, $N$ 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 2000: 11F11