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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
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Mathematical Citation Quotient (MCQ) 2017: 0.62

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Volume 16, Issue 2


Totally isotropic subspaces of small height in quadratic spaces

Wai Kiu Chan / Lenny Fukshansky
  • Corresponding author
  • Department of Mathematics, 850 Columbia Avenue, Claremont McKenna College, Claremont, CA 91711, USA
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/ Glenn R. Henshaw
  • Department of Mathematics, Engineering and Computer Science, LaGuardia Community College, 31-10 Thomson Avenue, Long Island City, NY 11101, USA
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Published Online: 2016-04-16 | DOI: https://doi.org/10.1515/advgeom-2015-0032


Let K be a global field or , let F be a nonzero quadratic form on KN with N ≥ 2, and let V be a subspace of KN.We prove the existence of an infinite collection of finite families of small-height maximal totally isotropic subspaces of (V, F) such that each such family spans V as a K-vector space. This result generalizes and extends a well known theorem of Vaaler [16] and further contributes to the effective study of quadratic forms via height in the general spirit of Cassels’ theorem on small zeros of quadratic forms. All bounds on the height are explicit.

Keywords: Heights; quadratic forms

About the article

Received: 2014-02-17

Revised: 2014-08-18

Published Online: 2016-04-16

Published in Print: 2016-04-01

Citation Information: Advances in Geometry, Volume 16, Issue 2, Pages 153–164, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0032.

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