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12:07 AM
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Q: Are there other Euclidean lattices whose construction is based on number theoretic identities?

mathoverflowUserIn the book of Conway and Sloane about Sphere packings and Lattices, which is referenced by the video of Borcherds a construction of the Leech Lattice based on the number theoretic identity: $$1^2+2^2+\cdots+24^2=70^2$$ is presented. I am asking myself if there are other lattices with possibly ot...

In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by John Leech (1967). It may also have been discovered (but not published) by Ernst Witt in 1940. == Characterization == The Leech lattice Λ24 is the unique lattice in 24-dimensional Euclidean space, E24, with the following list of properties: It is unimodular; i.e., it can be generated by the columns of a certain 24×24 matrix with determinant 1. It is even; i.e., the square of the length of each vector in Λ24 is...
 
 
16 hours later…
4:03 PM
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A: Help cleanup tags!

Sam HopkinsThe tag analytic-geometry is used for two different things: Euclidean geometry in coordinates; and a version of algebraic geometry where (according to my rough understanding) polynomials are replaced by power series so that you can do something like analysis. This is a genuine clash of mathematic...

 

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