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http://dx.doi.org/10.4134/JKMS.2007.44.1.055

ON THE INFINITE PRODUCTS DERIVED FROM THETA SERIES I  

Kim, Dae-Yeoul (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University)
Koo, Ja-Kyung (Department of Mathematics Korea Advanced Institute of Science and Technology)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.1, 2007 , pp. 55-107 More about this Journal
Abstract
Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.
Keywords
transcendental number; algebraic number; theta series; Rogers-Ramanujan identities;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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