Oleg Pikhurko

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20242026

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math.MG2025

New upper bound for lattice covering by spheres

Jun Gao, Xizhi Liu, Oleg Pikhurko +1

We show that there exists a lattice covering of $R^{n}$ by Eucledian spheres of equal radius with density $O (n ln^{2} n)$ as $n \to \infty$ , where \begin{align*} Î²:=…

math.MG2025

Fractional Divisibility of Spheres with Partially Generic Sets of Rotations

Jan GrebÃk, Christian Ikenmeyer, Oleg Pikhurko

We say that an r-tuple $(g_{1}, ..., g_{r})$ of special orthogonal $d \times d$ matrices fractionally divides the $(d - 1)$ -dimensional sphere $S$ if there is a non-constant function in $L^…