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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

Rainer Dietmann
Rainer Dietmann*
Affiliation:
Institut für Algebra und Zahlentheorie, Pfaffenwaldring 57, D-70550 Stuttgart, Germany e-mail: dietmarr@mathematik.uni-stuttgart.de
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Abstract

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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 $m$.

Keywords

11D0911E1211H4611H55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 63 - 65
Copyright
Copyright © Canadian Mathematical Society 2009

References

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