Non-Archimedean Brauer Oval (of Cassini) Theorem and Applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917189088444416 |
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| author | Krishna, K. Mahesh |
| author_facet | Krishna, K. Mahesh |
| contents | Nica and Sprague [\textit{Am. Math. Mon., 2023}] derived a non-Archimedean version of the Gershgorin disk theorem. We derive a non-Archimedean version of the oval (of Cassini) theorem by Brauer [\textit{Duke Math. J., 1947}] which generalizes the Nica-Sprague disk theorem. We provide applications for bounding the zeros of polynomials over non-Archimedean fields. We also show that our result is equivalent to the non-Archimedean version of the Ostrowski nonsingularity theorem derived by Li and Li [\textit{J. Comput. Appl. Math., 2025}]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_04228 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Archimedean Brauer Oval (of Cassini) Theorem and Applications Krishna, K. Mahesh Number Theory Functional Analysis 15A18, 15A42, 12J25, 26E30 Nica and Sprague [\textit{Am. Math. Mon., 2023}] derived a non-Archimedean version of the Gershgorin disk theorem. We derive a non-Archimedean version of the oval (of Cassini) theorem by Brauer [\textit{Duke Math. J., 1947}] which generalizes the Nica-Sprague disk theorem. We provide applications for bounding the zeros of polynomials over non-Archimedean fields. We also show that our result is equivalent to the non-Archimedean version of the Ostrowski nonsingularity theorem derived by Li and Li [\textit{J. Comput. Appl. Math., 2025}]. |
| title | Non-Archimedean Brauer Oval (of Cassini) Theorem and Applications |
| topic | Number Theory Functional Analysis 15A18, 15A42, 12J25, 26E30 |
| url | https://arxiv.org/abs/2601.04228 |