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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>)
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
Center for Undergraduate Studies, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
- 1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
- 2 Center for Undergraduate Studies, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
Applied Mathematics·Volume 05 (2014)·Pages 1284–1291·Published 24 April 2014·DOI10.4236/am.2014.58120
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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 k 2 m. 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.
KeywordsQuadratic IrrationalsHecke GroupsLegendre Symbol<i>G</i>-Set
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