A p-adic Poissonian Pair Correlation Concept

TL;DR

This paper introduces a p-adic generalization of the Poissonian pair correlation concept, exploring its properties and connections to p-adic discrepancy theory, expanding the understanding of uniform distribution in p-adic settings.

Contribution

It proposes a novel p-adic pair correlation framework and investigates its fundamental properties and links to discrepancy theory, extending classical concepts to p-adic integers.

Findings

Established basic properties of p-adic pair correlation

Connected p-adic correlation to discrepancy theory

Provided foundational results for future research

Abstract

The pair correlation statistic is an important concept in real uniform distribution theory. Therefore, sequences in the unit interval with (weak) Poissonian pair correlations have attracted a lot of attention in recent time. The aim of this paper is to suggest a generalization to the p-adic integers and to prove some of its main properties. In particular, connections to the theory of p-adic discrepancy theory are discussed.