대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권1호
  • /
  • Pages.55-107
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  • 2007
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2007.01.31
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초록

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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참고문헌

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피인용 문헌

  1. REMARKS FOR BASIC APPELL SERIES vol.31, pp.4, 2009, https://doi.org/10.5831/HMJ.2009.31.4.463
  2. DIVISOR FUNCTIONS AND WEIERSTRASS FUNCTIONS ARISING FROM q-SERIES vol.49, pp.4, 2012, https://doi.org/10.4134/BKMS.2012.49.4.693
  3. A note on the transcendence of infinite products vol.62, pp.3, 2012, https://doi.org/10.1007/s10587-012-0053-2