Arithmetic of infinite products and Rogers-Ramanujan continued fractions
Commun. Korean Math. Soc. 2007 Vol. 22, No. 3, 331-351
Printed September 1, 2007
Daeyeoul Kim, Ja Kyung Koo, Yilmaz Simsek
Chonbuk National University, Korea Advanced Institute of Science and Technology, University of Akdeniz
Abstract : 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
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