M\"{o}bius disjointness for a class of exponential functions

TL;DR

This paper demonstrates that a broad class of exponential functions, including polynomial-like and piece-wise polynomial functions, are deterministic and largely disjoint from the Möbius function, advancing understanding in number theory and dynamical systems.

Contribution

It introduces a new class of exponential functions shown to be deterministic and proves their disjointness from the Möbius function, extending previous disjointness results.

Findings

Many exponential functions are deterministic.

These functions are disjoint from the Möbius function.

The class includes functions with polynomial-like exponents.

Abstract

A vast class of exponential functions are shown to be deterministic. This class includes functions whose exponents are polynomial-like or "piece-wise" close to polynomials after differentiation. Many of these functions are proved to be disjoint from the M\"obius function.