Geometric Considerations in Lattice Programming

Moritz Andreas Venzin
2023
EPFL thesis

Abstract

We provide faster algorithms and fine-grained reductions for lattice problems in general norms.

Official source

https://infoscience.epfl.ch/record/300547?ln=en

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

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

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

Geometric Considerations in Lattice Programming

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

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

BLOOM: Bimodal Lattice One-out-of-Many Proofs and Applications

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

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

BLOOM: Bimodal Lattice One-out-of-Many Proofs and Applications