The structure of weight and function classes with coprime bases

TL;DR

This paper extends a number theory framework to construct measures that are simultaneously $m$-adic and $n$-adic doubling for coprime integers, yet not doubling, and explores their implications for weight and function classes.

Contribution

It generalizes previous constructions to coprime bases and reveals new applications in weight and function class intersections.

Findings

Constructed measures that are $m$-adic and $n$-adic doubling for coprime $m,n$ but not doubling

Extended the number theory framework for broader applicability

Identified new applications to weight and function class intersections

Abstract

In a recent work of Anderson and Hu, the authors constructed a measure that was $p$-adic and $q$-adic doubling, for any primes $p$ and $q$, yet not doubling. This work relied heavily on a developed number theory framework. Here we develop this framework farther, which yields a measure that is $m$-adic and $n$-adic doubling for any coprime $m,n$, yet not doubling. Additionally we show several new applications to the intersection of weight and the function classes.