Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2007.01.31
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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.

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References

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