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Date: 17-8-2020
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Date: 30-12-2019
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Date: 10-5-2020
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The group of all Möbius transformations of the form
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(1) |
where ,
,
, and
are integers with
. The group can be represented by the
matrix
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(2) |
where . Every
can be expressed in the form
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(3) |
where
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(4) |
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(5) |
although the representation is not unique (Apostol 1997, pp. 28-29).
REFERENCES:
Apostol, T. M. "The Modular Group and Modular Functions." Ch. 2 in Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 17 and 26-46, 1997.
Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, p. 113, 1987.
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