关于多线性多项式的零点
On zeros of multilinear polynomials
摘要：
我们考虑多变量多项式在一个固定的数域，线性的一些变量。对于这样的多项式满足一定的技术条件的系统，我们证明了存在的搜索边界的同时零的高度。对于一个单一的这样的多项式，我们证明了存在的搜索范围就高度为零躺在一个规定的代数集之外。我们还获得了搜索界的情况下，齐次多线性多项式，这是一个所谓的“稀疏”版本的西格尔引理。在我们开发的工具中，高度不等式是一些独立的兴趣。
英文摘要：
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with respect to height. For a single such polynomial, we prove the existence of search bounds with respect to height for zeros lying outside of a prescribed algebraic set. We also obtain search bounds in the case of homogeneous multilinear polynomials, which are related to a so-called "sparse" version of Siegel's lemma. Among the tools we develop are height inequalities that are of some independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
