Modular Group Gamma
المؤلف:
Apostol, T. M.
المصدر:
"The Modular Group and Modular Functions." Ch. 2 in Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
24-12-2019
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Modular Group Gamma
The group 
of all Möbius transformations of the form
 |
(1)
|
where 
, 
, 
, and 
are integers with 
. The group can be represented by the 
matrix
![A=[a b; c d],](http://mathworld.wolfram.com/images/equations/ModularGroupGamma/NumberedEquation2.gif) |
(2)
|
where 
. Every 
can be expressed in the form
 |
(3)
|
where
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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