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math.NT2026
A cyclotomic gluing construction for lattice sphere packings
Nihar Gargava, Matthias Gröbner, Michael Simkin
For a positive integer , let denote the supremum of the densities of lattice sphere packings in . We prove that, for every sufficiently large , $Δ_d^L \g…
math.NT2025
Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere
Claire Burrin, Matthias Gröbner
We study the distribution of rational points of fixed height on the sphere at shrinking scales. For the two-dimensional sphere, we prove an unconditional variance estimate for prim…
math.NT2024
Rational points on ellipsoids and modular forms
Claire Burrin, Matthias Gröbner
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and oth…