Small Zeros of Quadratic Forms with Linear Conditions

Details Small Zeros of Quadratic Forms with Linear Conditions Small Zeros of Quadratic Forms with Linear Conditions

2004-02-17

arxiv.org/abs/math/0402284v1

J. Number Theory 108 (2004), no. 1, 29--43

Mathematics

Number Theory

11 pages, to appear in Journal of Number Theory

Scientific paper

Given a quadratic form and $M$ linear forms in $N+1$ variables with coefficients in a number field $K$, suppose that there exists a point in $K^{N+1}$ at which the quadratic form vanishes and all the linear forms do not. Then we show that there exists a point like this of relatively small height. This generalizes a result of D.W. Masser (1998). As a corollary of this result, we prove an extension of Cassels' theorem on small zeros of quadratic forms (1955) to non-singular small zeros over a number field.

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