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- W1984445793 abstract "Let Ω denote the projective line over the real quadratic field and δ denote the projective line over the finite field Fq with q elements. Coset diagrams for the orbits of the modular group G acting on Ω and δ give some interesting information. By using these diagrams we determine a condition for the existence of an orbit of G on Ω containing a circuit of a given type. If such a circuit exists, we find a condition under which the orbit contains a real quadratic irrational number α along with its algebraic conjugate ᾱ. As there are two projections from Ω to δ we are interested in the case when G acts on δ and we determine necessary and sufficient conditions for the existence of two orbits of G: one containing α along with 1/α and the other containing α together with 1/ᾱ." @default.
- W1984445793 created "2016-06-24" @default.
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- W1984445793 date "1998-01-01" @default.
- W1984445793 modified "2023-09-27" @default.
- W1984445793 title "On word structure of the modular group over finite and real quadratic fields" @default.
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- W1984445793 doi "https://doi.org/10.1016/s0012-365x(97)81824-9" @default.
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