Communications of the
Korean Mathematical Society CKMS

Let $k$ be an imaginary quadratic field, $\frak h$ the complex upper half plane, and let $\tau\in \frak h \cap k$, $q=e^{\pi i \tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

Keywords: transcendental number, algebraic number, theta series, Rogers-Ramanujan continued fraction

MSC numbers: 11Jxx, 11R04, 11F11