Gamma Group

The gamma group $\Gamma$ is the set of all transformations $w$ of the form

$$w(t)={at+b\over ct+d},$$

where $a$, $b$, $c$, and $d$ are Integers and $ad-bc=1$.

See also Klein's Absolute Invariant, Lambda Group, Theta Function

References

Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, pp. 127-132, 1987.