On Subsets of Q(√m) Q under the Action of Hecke Groups H(λq) - Applied Mathematics

AM > Vol.5 No.8, May 2014

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

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Download as PDF (Size: 447KB) PP. 1284-1291

DOI: 10.4236/am.2014.58120 3,771 Downloads 4,947 Views Citations

Author(s)

M. Aslam Malik, M. Asim Zafar

Affiliation(s)

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.

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

Share and Cite:

m) Q under the Action of Hecke Groups H(λ_q)">

Malik, M. and Zafar, M. (2014) On Subsets of Q(√m) Q under the Action of Hecke Groups H(λ_q). Applied Mathematics, 5, 1284-1291. doi: 10.4236/am.2014.58120.

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