Non-Archimedean Brauer Oval (of Cassini) Theorem and Applications
Number Theory
2026-01-09 v1 Functional Analysis
Abstract
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}].
Cite
@article{arxiv.2601.04228,
title = {Non-Archimedean Brauer Oval (of Cassini) Theorem and Applications},
author = {K. Mahesh Krishna},
journal= {arXiv preprint arXiv:2601.04228},
year = {2026}
}
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14 Pages, 0 Figures