Note on adelic triangulations and an Adelic Blichfeldt-type inequality

TL;DR

This paper introduces a new framework for convex geometry in adelic spaces, leading to an adelic version of Blichfeldt's inequality that extends previous results in the field.

Contribution

It defines convex hulls and polytopes in adelic spaces and develops adelic triangulations, resulting in a novel adelic Blichfeldt-type inequality.

Findings

Established a notion of convex hull and polytope in adelic space

Developed adelic triangulations for geometric analysis

Proved an adelic Blichfeldt-type inequality

Abstract

We introduce a notion of convex hull and polytope into adele space. This allows to consider adelic triangulations which, in particular, lead to an adelic blichfeldt-type inequality, complementing former results.