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Thursday, November 16, 2023

WEEK 11

Area of coronas and a Zeta funtion

A=\frac{\pi}{2}\; \sum_{\mathbf f\in \mathbb Z^2_o} \frac{1}{\left(\|\mathbf M\mathbf f \|^2 - B\right)^2}

where \mathbf a and \mathbf b are two adjacent spionors in a corona,  \mathbf M= [\mathbf a|\mathbf b], and B=\pm \,\mathbf a\times \mathbf b.

The figure below shows spinors around the disk of curvature B=23 in the Apollonian Window.  Initial spins may be chosen \mathbf a = [1,\, 5] and \mathbf b = [3, -4]



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