M\"{o}bius disjointness for a class of exponential functions
Number Theory
2022-07-07 v3
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.
Keywords
Cite
@article{arxiv.2011.08699,
title = {M\"{o}bius disjointness for a class of exponential functions},
author = {Weichen Gu and Fei Wei},
journal= {arXiv preprint arXiv:2011.08699},
year = {2022}
}
Comments
37 pages. To better understand the main results of this paper, we split it into two independent papers. The second paper is arXiv:2101.10134. The paper is accepted by The Quarterly Journal of Mathematics at https://doi.org/10.1093/qmath/haac009