Zoom Meeting ID: 818 0514 4375

Abstract. We study the continued fractions I1(τ ) and I2(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 I1(τ ) and I2(τ ) to find the relation with the generator of the field of modular functions on Γ0(16). Moreover we prove that the values 2(I1(τ )2 + 1/I1(τ )2 ) and 2(I2(τ ) 2 + 1/I2(τ )2 ) are algebraic integers for certain imaginary quadratic quantity τ .