论文标题
多线性多项式的零
On zeros of multilinear polynomials
论文作者
论文摘要
我们考虑在固定数字字段上的多元多项式，在某些变量中线性。对于满足某些技术条件的这种多项式系统的系统，我们证明了相对于高度的同时零的搜索范围。对于单个这样的多项式，我们证明了搜索边界相对于位于规定的代数集外的零的高度的存在。在均质的多项式多项式情况下，我们还获得了搜索范围，该域与Siegel的诱饵的所谓“稀疏”版本有关。我们开发的工具包括高度不平等，具有独立的兴趣。
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.
