Year: 2000
Type: preprint
Abstract: Suppose L is any finite algebraic extension of either the ordinary rational numbers or the p-adic rational numbers. Also let g_1,...,g_k be polynomials in n variables, with coefficients in L, such that the total number of monomial terms appearing in at least one g_i is exactly m. We prove that the maximum number of isolated roots of G:=(g_1,...,g_k) in L^n is finite and depends solely on (m,n,L), i.e., is independent of the degrees of the g_i. We thus obtain an arithmetic analogue of Khovanski's Theorem on Fewnomials, extending earlier work of Denef, Van den Dries, Lipshitz, and Lenstra.
Source: arXiv (Cornell University)
Author: Rojas, J. Maurice
Institution: Texas A&M University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394647271