Ramanujan continued fractions of order sixteen.

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 Γ 0 (1 6). Moreover we prove that the values 2 (I 1 (τ) 2 + 1 / I 1 (τ) 2) and 2 (I 2 (τ) 2 + 1 / I 2 (τ) 2) are algebraic integers for certain imaginary quadratic quantity τ. [ABSTRACT FROM AUTHOR]