Modular Group Lambda

The set  of linear Möbius transformations  which satisfy

where  and  are odd and  and  are even.  is a subgroup of the modular group Gamma, and is also called the theta subgroup. The fundamental region of the modular lambda group is illustrated above.

REFERENCES:

Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, pp. 113-114, 1987.