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Saturday, May 24, 2025

Entry 83

Level 13. Define dk=η(kτ) with Dedekind eta function η(kτ) and the McKay-Thompson series of class 13B j13B(τ)=(d1d13)2

Examples. Let d=13m with class number h(d)=2 for m=7,31 and we find a phenomenon similar to Level 5 j13B(1+7/132)=13(3+132)j13B(1+31/132)=13(3+132)3

But where Class 5B involves the fundamental unit U5 or the golden ratio, Class 13B involves U13=3+132 also known as the bronze ratio.

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