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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 5 > No. 1


Certain Types of the Orbits of Real Quadratic Fields by Hecke Groups

PP: 93-97
M. Asim Zafar, M. Aslam Malik,
Erich Hecke (1936) introduced the groups H(lq) = hS,T : S2 = Tq = 1i generated by two linear-fractional transformations S(z) = −1 z and T(z) = −1 z+l . In this paper, we discuss the action of hecke groups H(lq) on real quadratic fields. In particular, we explore the orbits of Q(√m)\Q where Q(√m)\Q is the disjoint union of Q∗(√n)={ a+√n c : a, c 6=0,b = a2−n c ∈ Z | (a,b, c)=1} for n=k2m.

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