Noah Stephens-Davidowitz

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20182026

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math.MG2026

Lattices with Large Kissing Number from Local Density

Huck Bennett, Minki Hhan, Zihan Li +1

Let $κ_{p} (n)$ denote the maximum kissing number of a lattice $L \subset R^{n}$ . We prove that $κ_{p} (n) \geq 2^{Ω (n)}$ for all $p \geq 1$ and that $κ_p(n) \geq Ω…

math.MG2018

Kissing numbers and transference theorems from generalized tail bounds

Stephen D. Miller, Noah Stephens-Davidowitz

We generalize Banaszczyk's seminal tail bound for the Gaussian mass of a lattice to a wide class of test functions. From this we obtain quite general transference bounds, as well a…