Date: 5월 28일 (금) 15:30~16:30
Place: Zoom (ID: 818 0514 4375)
Speaker : 박윤경 (서울과학기술대학교)
Title: Ramanujan continued fractions of order sixteen
We study the continued fractions $I_1(\tau)$ and $I_2(\tau)$ of order sixteen by adopting the theory of modular functions. These functions are analogues of Rogers--Ramanujan continued fraction $r(\tau)$ with modularity and many interesting properties. Here we prove the modularities of $I_1(\tau)$ and $I_2(\tau)$ to find the relation with the generator of the field of modular functions on $\Gamma_0(16)$. Moreover we prove that the values $2(I_1(\tau)^2 + 1/I_1(\tau)^2)$ and $2(I_2(\tau)^2+1/I_2(\tau)^2)$ are algebraic integers for certain imaginary quadratic quantity $\tau$.