CSUN Algebra, Number Theory, and Discrete Mathematics Seminar

Given an isotropic integral quadratic form which assumes a value $t$, we investigate the distribution of integer points at which this values 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 $t$. This is joint work with W. K. Chan.