Small representations of integers by integral quadratic forms

Abstract

Given an isotropic quadratic form over a number field which assumes a value t, we investigate the distribution of points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of quadratic forms, we produce bounds on height of points outside of some algebraic sets in a quadratic space at which the form assumes the value t. Our bounds on height are explicit in terms of the heights of the form, the space, the algebraic set and the value t.