Loading [MathJax]/jax/output/HTML-CSS/jax.js

Thursday, October 31, 2019

Entry 41

Define dk=η(kτ) with the Dedekind eta function η(τ). Then for Level 6 (d22d3d1d26)41=(d2d33d1d36)3(d22d3d1d26)49=(d51d3d2d56) Expressed as the triple of eta quotients (a,b,c) such that a1=ba9=c then (m,n)=(1,9) and abc=(d2d3d1d6)12bca=(d1d3d2d6)6acb=(d1d2d3d6)4 where (a,b,c) are the McKay-Thompson series of class 6E (A105559A128633). They obey (64abc+bca)+2a=abc+bca+acb which is one of the 9 dependencies found by Conway, Norton, and Atkin such that the moonshine functions span a linear space of 1729=163 dimensions. Similar identities involving only moonshine functions exist for levels (6,10,12,18,30).

No comments:

Post a Comment