On Subsets of Q(√m) Q under the Action of Hecke Groups H(λ_q)

M. Aslam Malik, M. Asim Zafar

Center for Undergraduate Studies, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.

DOI: 10.4236/am.2014.58120                

Abstract

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 the action of on for finding different orbits.

Keywords

Quadratic Irrationals, Hecke Groups, Legendre Symbol, G-Set

Conflicts of Interest

The authors declare no conflicts of interest.

References

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