Partition regularity in imaginary quadratic rings of integers
Combinatorics
2026-04-08 v2 Dynamical Systems
Number Theory
Abstract
We obtain partition regularity results for homogeneous quadratic equations whose parametrized solutions admit nice factorizations into linear forms over rings of integers of imaginary quadratic fields. To do so, we develop number-theoretic results of independent interest on such fields, such as a characterization for aperiodic completely multiplicative functions, the Tur\'an-Kubilius inequality, and a new concentration estimate for multiplicative functions.
Keywords
Cite
@article{arxiv.2603.20497,
title = {Partition regularity in imaginary quadratic rings of integers},
author = {Sebastián Donoso and Andreu Ferré Moragues and Andreas Koutsogiannis and Wenbo Sun},
journal= {arXiv preprint arXiv:2603.20497},
year = {2026}
}
Comments
40 pages. Comments welcome!