Thanks for clicking through… I guess.
If nothing else, it shows that just as much as the stock market is fueled by greed, mathematical reasearch is driven by frustration (or the pleasure gained from knowing others to be frustrated).
I did spend the better part of the day doing a lengthy, if not laborious, calculation, I’ve been postponing for several years now. Partly, because I didn’t know how to start performing it (though the basic strategy was clear), partly, because I knew beforehand the final answer would probably offer me no further insight.
Still, it gives the final answer to a problem that may be of interest to anyone vaguely interested in Moonshine :
What does the Monster see of the modular group?
I know at least two of you, occasionally reading this blog, understand what I was trying to do and may now wonder how to repeat the straightforward calculation. Well the simple answer is : Google for the number 97239461142009186000 and, no doubt, you will be able to do the computation overnight.
One word of advice : don’t! Get some sleep instead, or make love to your partner, because all you’ll get is a quiver on nine vertices (which is pretty good for the Monster) but having an horrible amount of loops and arrows…
If someone wants the details on all of this, just ask. But, if you really want to get me exited : find a moonshine reason for one of the following two numbers :
$791616381395932409265430144165764500492= 2^2 * 11 * 293 * 61403690769153925633371869699485301 $
(the dimension of the monster-singularity upto smooth equivalence), or,
$1575918800531316887592467826675348205163= 523 * 1655089391 * 15982020053213 * 113914503502907 $
(the dimension of the moduli space).
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