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 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 Downloads: Full-text PDF

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