[Seminar 2021.05.28] Ramanujan continued fractions of order sixteen

by qsms posted May 21, 2021


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일정시작 2021-05-28
일정종료 2021-05-28
배경색상 #FF5733

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 $\tau$.







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