Geodesic
Small Zeros of Quadratic Forms Avoiding a Finite Number of Prescribed Hyperplanes
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 63-65

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DOI

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 $m$ .
DOI : 10.4153/CMB-2009-007-7
Mots-clés : 11D09, 11E12, 11H46, 11H55 
Dietmann, Rainer. Small Zeros of Quadratic Forms Avoiding a Finite Number of Prescribed Hyperplanes. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 63-65. doi: 10.4153/CMB-2009-007-7
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     author = {Dietmann, Rainer},
     title = {Small {Zeros} of {Quadratic} {Forms} {Avoiding} a {Finite} {Number} of {Prescribed} {Hyperplanes}},
     journal = {Canadian mathematical bulletin},
     pages = {63--65},
     year = {2009},
     volume = {52},
     number = {1},
     doi = {10.4153/CMB-2009-007-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-007-7/}
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