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Certain Types of the Orbits of Real Quadratic Fields by Hecke Groups |
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PP: 93-97 |
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doi:10.18576/msl/050113
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Author(s) |
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M. Asim Zafar,
M. Aslam Malik,
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Abstract |
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| 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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