Exponential sums of the M\"{o}bius function and flat polynomials
Number Theory
2022-01-07 v3 Dynamical Systems
Abstract
We present an elementary problem on analytic polynomials with coefficients or in which implies Riemann hypothesis. It is turns out that this problem is a particular case of the weak form of a flat polynomials problem asked by Erd\"os in his 1957's paper. We provide also under an extra-condition the converse.
Cite
@article{arxiv.1910.10569,
title = {Exponential sums of the M\"{o}bius function and flat polynomials},
author = {el Houcein el Abdalaoui},
journal= {arXiv preprint arXiv:1910.10569},
year = {2022}
}
Comments
8 pages. The motivation of the study of the polynomials with Liouville or M\"obius coefficients is added and the results is linked to P\'olya's approach to the Riemann hypothesis and several results on the maximum of those polynomials under GRH due essentially to Hajela and Smith. Some misprints and notations are corrected