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Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Vlad Serban, Nihar Prakash Gargava

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Espace pseudo-euclidien

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Geometric Learning: Leveraging differential geometry for learning and control

Anomalous and Chern topological waves in hyperbolic networks

Mean value theorems for collections of lattices with a prescribed group of symmetries

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

A structured prediction approach for robot imitation learning

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

Moments of the number of points in a bounded set for number field lattices

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Relative, local and global dimension in complex networks

Anomalous and Chern topological waves in hyperbolic networks

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Mean value theorems for collections of lattices with a prescribed group of symmetries

Geometric Learning: Leveraging differential geometry for learning and control

Moments of the number of points in a bounded set for number field lattices

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

A structured prediction approach for robot imitation learning

Relative, local and global dimension in complex networks

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control