P-adic Poissonian Pair Correlations via the Monna Map

TL;DR

This paper explores how to transfer sequences with Poissonian pair correlations from the real numbers to the p-adic integers using the Monna map, providing a method to construct explicit examples.

Contribution

It introduces a novel approach to generate p-adic sequences with Poissonian pair correlations from known real sequences via the Monna map.

Findings

Transfer method for real to p-adic sequences with Poissonian correlations

Explicit construction of p-adic sequences with desired correlation properties

Bridging real and p-adic sequence analysis

Abstract

Although the existence of sequences in the p-adic integers with Poissonian pair correlations has already been shown, no explicit examples had been found so far. In this note we discuss how to transfer real sequences with Poissonian pair correlations to the p-adic setting by making use of the Monna map.