Work

Multiple sums with the Möbius function

Year: 2025

Type: article

Abstract: ABSTRACT We establish nontrivial bounds for bilinear sums involving the Möbius function evaluated over solutions to a broad class of equations. Several of our results may be regarded as Möbius-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.

Source: The Quarterly Journal of Mathematics

DOI: 10.1093/qmath/haaf049

Authors: William D Banks, Igor E Shparlinski

Institutions: University of Missouri, UNSW Sydney

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Division of Arctic Sciences

Awards: G4172890344, G733670931