Modular Gamma Function

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 $ad-bc=1$. $\Gamma$-modular functions are then defined as in Borwein and Borwein (1987, p. 114).

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.