Upper Half-Plane

The upper half-plane is the portion of the complex plane  satisfying  i.e., . Common notations include , , , and  (Borwein and Borwein 1987, pp. 112 and 398).

The notation  or  is sometimes used to denote  (Borwein and Borwein 1987, pp. 112 and 398).

REFERENCES:

Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, p. 14, 1997.

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