Gaussian Mass Maximality of the Integer Lattice
Prior state unknown→proved
integral unimodular lattices of rank at most 32; the general conjecture is open
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number-theory / Geometry of numbers
Gaussian Mass Maximality of the Integer Lattice
Regev and Stephens-Davidowitz conjectured that $\mathbb{Z}^n$ maximizes the Gaussian mass $\Theta_L(t) = \sum_{x \in L} e^{-t\|x\|^2}$ over stable lattices for every $t > 0$. The sharp inequality holds for every integral unimodular lattice of rank $n \le 32$, with equality only at $\mathbb{Z}^n$.
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Regev and Stephens-Davidowitz conjectured that $\mathbb{Z}^n$ maximizes the Gaussian mass $\Theta_L(t) = \sum_{x \in L} e^{-t\|x\|^2}$ over stable lattices for every $t > 0$. The sharp inequality holds for every integral unimodular lattice of rank $n \le 32$, with equality only at $\mathbb{Z}^n$.
integral unimodular lattices of rank at most 32; the general conjecture is open
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