Abstract
AbstractWe 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.
Publisher
Canadian Mathematical Society
Cited by
4 articles.
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1. Small representations of integers by integral quadratic forms;Journal of Number Theory;2019-08
2. Espaces adéliques quadratiques;Mathematical Proceedings of the Cambridge Philosophical Society;2016-06-29
3. Small zeros of quadratic forms outside a union of varieties;Transactions of the American Mathematical Society;2014-04-01
4. Heights and quadratic forms: Cassels’ theorem and its generalizations;Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms;2013