Communications of the
Korean Mathematical Society CKMS

Let $\frak h$ be the complex upper half plane, let $h(\tau)$ be a cusp form, and let $\tau$ be an imaginary quadratic in $\frak h$. If $h(\tau)$ $\in$ $\Omega$ $( g_2 (\tau)^m g_3 (\tau)^l )$ with $\Omega$ the field of algebraic numbers and $m,l$ positive integers then, we shall show that $h(\tau)$ is integral over the ring $\Bbb Q [h(\frac{\tau}{n})$ $\cdots$ $h(\frac{\tau +n-1}{n})]$.

Keywords: algebraic integer, cusp form, Eisenstein series

MSC numbers: 11R04, 11F11