Bulletin of the
Korean Mathematical Society BKMS

As a by-product of [5], we produce algebraic integers of certain values of quotients of Eisenstein series. And we consider the relation of $\theta_3 (0,\tau)$ and $\theta_3 (0,\tau^n )$. That is, we show that $\vert\theta_3 (0,\tau^n )\vert$ $=\vert\theta_3 (0,\tau)\vert$, $\Delta (0,\tau)= \Delta (0,\tau^n )$ and $J(\tau)=J(\tau^n)$ for some $\tau \in \frak h$.

Keywords: infinite product, Eisenstein series, theta series

MSC numbers: 11R04, 11F11