Additive bases arising from functions in a Hardy field

TL;DR

This paper extends the concept of additive bases to a broader class of functions from Hardy fields, demonstrating that these functions form asymptotic bases, thus generalizing classical results like Waring's problem.

Contribution

It introduces a new class of functions from Hardy fields as additive bases, expanding the scope beyond polynomial and power sequences.

Findings

Functions from Hardy fields are asymptotic bases.

Generalization of classical additive basis results.

Broader applicability to non-polynomial functions.

Abstract

A classical additive basis question is Waring's problem. It has been extended to integer polynomial and non-integer power sequences. In this paper, we will consider a wider class of functions, namely functions from a Hardy field, and show that they are asymptotic bases.