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Small Zeros of Quadratic Forms Avoiding a Finite Number of Prescribed Hyperplanes
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove a new upper bound for the smallest zero $x$ of a quadratic form over a number field with the additional restriction that $x$ does not lie in a finite number of $m$ prescribed hyperplanes. Our bound is polynomial in the height of the quadratic form, with an exponent depending only on the number of variables but not on $m$.
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- Copyright © Canadian Mathematical Society 2009
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