Bull. Korean Math. Soc. 2002; 39(2): 299-307
Printed June 1, 2002
Copyright © The Korean Mathematical Society.
Daeyeoul Kim and Ja Kyung Koo
Chonbuk National University, Korea Advanced Institute of Science and Technology
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
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