E23

The u-invariant of a rational function field over a field k can be expressed in terms of the invariant u_k(2,n) that gives the number of variables needed for a pair of quadratic forms to vanish on an n-dimensional vector space defined over k. New estimates for u_k(2,n) will be given. When k is algebraically closed, a very elementary method will be given to recover some classical results in algebraic geometry.

Prof. Dr. David Leep

University of Kentucky, Lexington, USA