Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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RAMANUJAN CONTINUED FRACTIONS OF ORDER EIGHTEEN

  • Yoon Kyung Park (School of Natural Sciences Seoul National University of Science and Technology)
  • Received : 2022.04.14
  • Accepted : 2023.01.16
  • Published : 2023.03.01
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Abstract

As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(𝜏). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

Keywords

Acknowledgement

This study was financially supported by NRF 2021R1F1A1055200.

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