Physical Sciences and Mathematics Commons^™

Height Bounds On Zeros Of Quadratic Forms Over Q-Bar, Lenny Fukshansky

CMC Faculty Publications and Research

In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For a single quadratic form in N ≥ 2 variables on a subspace of Q N , we prove an upper bound on the height of a smallest nontrivial zero outside of an algebraic set under the assumption that such a zero exists. For a system of k quadratic forms on an L-dimensional subspace of Q N , N ≥ L ≥ k(k+1) 2 + 1, we prove existence of a nontrivial simultaneous small-height zero. For a system of one or two inhomogeneous quadratic and …