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 \( 2r^{2} + 3r \).
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Received: 22 August 2002; revised manuscript accepted: 11 August 2003