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On Subsets of Q(√<span style=" text-decoration:overline;">m</span>) Q under the Action of Hecke Groups H(λ<sub>q</sub>)
is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two Hecke groups—the full modular group and the group of linear-fractional transformations on . In particular, we investigate …