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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


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.

© 1996-9 Eric W. Weisstein