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Archiv der Mathematik

, Volume 82, Issue 6, pp 507–516 | Cite as

Systems of rational quadratic forms

  • R.  Dietmann
Original paper

Abstract.

We improve a result by W. Schmidt, giving a sufficient condition for a system of rational quadratic forms to have a non-trivial rational zero. For example every system of r rational quadratic forms has a non-trivial rational zero, provided that there exists a non-singular real zero and every form in the complex pencil has rank exceeding \( 2r^{2} + 3r \).

Mathematics Subject Classification (2000):

11D09 11D72 11E08. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Institut für Algebra und ZahlentheorieStuttgartGermany

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