Modular equations for congruence subgroups of genus zero (II)

We present a result that the modular equation of a Haupt-modul for a certain congruence subgroup Gamma(H) (N, t) of genus zero satisfies Kronecker's congruence relation. This generalizes the author's previous result about Gamma(1) (m) boolean AND Gamma(0) (MN). Furthermore we show that the similar result holds for a certain congruence subgroup F of genus zero with [Gamma : Gamma(H) (N, t)] = 2. Finally we prove a conjecture of Lee and Park, asserting that the modular equation of the continued fraction of order six satisfies a certain form of Kronecker's congruence relation. (C) 2020 Elsevier Inc. All rights reserved.