Counting rational linear spaces on hypersurfaces
by
Scott Parsell
Penn State University

We describe new estimates for the number of integral solutions of certain systems of symmetric diophantine equations, and we discuss applications to the problem of obtaining asymptotic estimates for the number of rational linear spaces of dimension d lying on the hypersurface c₁x₁^k + ... + c_sx_s^k=0, where c₁, ... , c_s are integers, and where s is sufficiently large in terms of k and d.

Date received: April 30, 2004