Modularity of a Ramanujan-Selberg continued fraction

Abstract

We study a Ramanujan-Selberg continued fraction S(tau) by employing the modular function theory. We first find modular equations of S(tau) of level n for every positive integer n by using affine models of modular curves. This is an extension of Baruah-Saikia's results for level n = 3, 5 and 7. We further show that the ray class field modulo 4 over an imaginary quadratic field K is obtained by the value of S-2(tau), and we prove the integrality of 1/S(tau) to find its class polynomial for K with tau is an element of K boolean AND h, where h is the complex upper half plane. (C) 2016 Elsevier Inc. All rights reserved.