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Wikipedia definition
1. Upper half-planeIn mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part y: The term is associated with a common visualization of complex numbers with points in the plane endowed with Cartesian coordinates, with the Y-axis pointing upwards: the "upper half-plane" corresponds to the half-plane above the X-axis. It is the domain of many functions of interest in complex analysis, especially modular forms.
Read “Upper half-plane” on English Wikipedia
Read “上半平面” on Japanese Wikipedia
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