Small Zeros of Quadratic Forms Avoiding a Finite Number of Prescribed Hyperplanes

Canadian mathematical bulletin

关键词: Ordered rings with involution;    $C^ast$-algebras and their representations;    noncommutative convexity theory;    real algebraic geometry;   

DOI  :  10.4153/CMB-2009-007-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove a new upper bound for the smallest zero $mathbf{x}$of a quadratic form over a number field with the additionalrestriction that $mathbf{x}$ does not lie in a finite number of $m$ prescribedhyperplanes. Our bound is polynomial in the height of the quadraticform, with an exponent depending only on the number of variables butnot on $m$.

【 授权许可】

Unknown