Bibliographic Details
| Title: |
Ramanujan's continued fractions of order 10 as modular functions. |
| Authors: |
Aricheta, Victor Manuel1 (AUTHOR) vmaricheta@math.upd.edu.ph, Guadalupe, Russelle1 (AUTHOR) rguadalupe@math.upd.edu.ph |
| Source: |
Journal of Number Theory. Jan2026, Vol. 278, p214-244. 31p. |
| Subjects: |
Continued fractions, Modular functions, Equations |
| Abstract: |
We explore the modularity of the continued fractions I (τ) , J (τ) , T 1 (τ) , T 2 (τ) , and U (τ) = I (τ) / J (τ) of order 10, which are special cases of certain identities of Ramanujan. The continued fractions I (τ) and J (τ) were recently introduced by Rajkhowa and Saikia. We show that these continued fractions can be expressed in terms of an η -quotient g (τ) that generates the field of all modular functions on the congruence subgroup Γ 0 (10). Consequently, we deduce that the modular equations for g (τ) and U (τ) exist at any level and derive these equations of prime levels p ≤ 11. We also show that the continued fractions of order 10 can be explicitly evaluated using a singular value of g (τ) , which under certain conditions generates the Hilbert class field of an imaginary quadratic field. We employ the methods of Lee and Park to establish our results. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
