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I've started looking into well-rounded Euclidean lattices and I was interested in learning whether their theta series have any interesting properties, but haven't found much in terms of bibliography or papers on the topic, is anyone aware of such material? Or is it maybe the case that their theta series are not that interesting, or has the same properties with other, more studied categories of lattices?

(One definition for well-rounded lattices: A (full-rank) $n$-dimensional Euclidean lattice is well-rounded if the $\mathbb{R}$-span of its set of vectors with minimal norm is $\mathbb{R}^n$)

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    $\begingroup$ Not much? Well-rounded lattices have the property that the span of the minimal vectors of the lattice is all of $\mathbb{R}^n$. So the behavior of the sums of vectors in the lattice is somehow more well-behaved than an arbitrary lattice. I don't see anything to say quantitatively however, and this condition feels weak. $\endgroup$
    – Josiah Park
    Commented Oct 17 at 2:39

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