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I've recently seen stated here https://en.wikipedia.org/wiki/Dedekind_eta_function#Definition, here https://math.stackexchange.com/a/1754273/917010, here: https://bahasa.wiki/nn/Dedekind_eta_function and in a couple more sites that there supposedly is a link between the Leech lattice, whose dimension is 24, and the 24 appearing in the expression of the Dedekind eta function.

The sentence is always the same: "The presence of 24 can be understood by connection with other occurrences, such as in the 24-dimensional Leech lattice." But there never is further explanation or a link to a refernce.

Does somebody knows what is this connection? If not could someone point an appropriate reference? I've tried looking on internet, in "A course in arithmetic" by Serre and in Apostol's book on modular forms but there was no mention of this.

Jabberwocky
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    The Wikipedia article Leech lattice gives an equation for the theta function of the lattice as $E_{12}(\tau)-\frac{65520}{691}\Delta(\tau)$. – Somos Jul 15 '22 at 01:22
  • See also "Where do the product expansions of modular forms come from?" https://mathoverflow.net/questions/129536/where-do-the-product-expansions-of-modular-forms-come-from – D.R. Dec 23 '22 at 19:36

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John Baez has great slides here, as he discusses "my favorite number $24$", connecting the Leech lattice, the Monster group, Dedekind's eta function and the value $\zeta(-1)$. The Leech lattice can be constructed from some $25$-dimensional lattice by using the vector $$ v=(0,1,2,3,\cdots ,24,70)\in \Bbb Z^{26}, $$ based on the identity $$ 0^2+1^2+2^2+3^2+\cdots +24^2=70^2. $$

Dietrich Burde
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