Multiple sums with the M\"obius function
Number Theory
2025-06-11 v1
Abstract
We establish nontrivial bounds for bilinear sums involving the M\"obius function evaluated over solutions to a broad class of equations. Several of our results may be regarded as M\"obius-function analogues of the ternary Goldbach problem. By contrast, the binary versions of our results remain out of reach, much like the binary Goldbach problem. Nevertheless, we make partial progress in this direction by restricting the range of the third variable as far as possible.
Cite
@article{arxiv.2506.08787,
title = {Multiple sums with the M\"obius function},
author = {William D. Banks and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:2506.08787},
year = {2025}
}
Comments
19 pages