Partition regularity in imaginary quadratic rings of integers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910106945323008 |
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| author | Donoso, Sebastián Moragues, Andreu Ferré Koutsogiannis, Andreas Sun, Wenbo |
| author_facet | Donoso, Sebastián Moragues, Andreu Ferré Koutsogiannis, Andreas Sun, Wenbo |
| contents | 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 Turán-Kubilius inequality, and a new concentration estimate for multiplicative functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partition regularity in imaginary quadratic rings of integers Donoso, Sebastián Moragues, Andreu Ferré Koutsogiannis, Andreas Sun, Wenbo Combinatorics Dynamical Systems Number Theory Primary: 05D10, Secondary:11N37, 11B30, 37A44 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 Turán-Kubilius inequality, and a new concentration estimate for multiplicative functions. |
| title | Partition regularity in imaginary quadratic rings of integers |
| topic | Combinatorics Dynamical Systems Number Theory Primary: 05D10, Secondary:11N37, 11B30, 37A44 |
| url | https://arxiv.org/abs/2603.20497 |