Upper Half-Plane
المؤلف:
Apostol, T. M
المصدر:
Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, p. 14, 1997.
الجزء والصفحة:
...
24-10-2018
994
Upper Half-Plane
The upper half-plane is the portion of the complex plane ![<span style=]()
{x+iy:x,y in (-infty,infty)}" src="http://mathworld.wolfram.com/images/equations/UpperHalf-Plane/Inline1.gif" style="height:14px; width:143px" /> satisfying ![y=I[z]>0](http://mathworld.wolfram.com/images/equations/UpperHalf-Plane/Inline2.gif)
i.e., ![<span style=]()
{x+iy:x in (-infty,infty),y in (0,infty)}" src="http://mathworld.wolfram.com/images/equations/UpperHalf-Plane/Inline3.gif" style="height:14px; width:193px" />. Common notations include 
, 
, 
, and 
(Borwein and Borwein 1987, pp. 112 and 398).
The notation 
or 
is sometimes used to denote ![H union <span style=]()
{iinfty} union Q" src="http://mathworld.wolfram.com/images/equations/UpperHalf-Plane/Inline10.gif" style="height:14px; width:85px" /> (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.
الاكثر قراءة في التحليل العقدي
اخر الاخبار
اخبار العتبة العباسية المقدسة
