Date | May 28, 2021 |
---|---|

Speaker | 박윤경 |

Dept. | 서울과학기술대학교 |

Room | 선택 |

Time | 15:30-16:30 |

**Zoom Meeting ID: 818 0514 4375**

Abstract. We study the continued fractions I_{1}(τ ) and I_{2}(τ ) of order sixteen by adopting the
theory of modular functions. These functions are analogues of Rogers-Ramanujan continued fraction
r(τ ) with modularity and many interesting properties. Here we prove the modularities of I_{1}(τ ) and
I_{2}(τ ) to find the relation with the generator of the field of modular functions on Γ0(16). Moreover
we prove that the values 2(I_{1}(τ )^{2} + 1/I_{1}(τ )^{2}
) and 2(I2(τ )
2 + 1/I_{2}(τ )^{2}
) are algebraic integers for
certain imaginary quadratic quantity τ .

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