Small zeros of hermitian forms over a quaternion algebra

  title={Small zeros of hermitian forms over a quaternion algebra},
  author={Wai Kiu Chan and Lenny Fukshansky},
Let D be a positive definite quaternion algebra over a totally real number field K, F (X, Y ) a hermitian form in 2N variables over D, and Z a right D-vector space which is isotropic with respect to F . We prove the existence of a small-height basis for Z over D, such that F (X, X) vanishes at each of the basis vectors. This constitutes a non-commutative analogue of a theorem of Vaaler [19], and presents an extension of the classical theorem of Cassels [1] on small zeros of rational quadratic… CONTINUE READING

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