ON THE U-INVARIANT OF P-ADIC FUNCTION FIELDS.

We show that a quadratic form defined over the rational function field ℚ( x 1 , ..., x n ) of dimension at least 4.2 n + 1 is isotropic over all fields ℚ p (x 1 , ..., x n ), except for finitely many primes. Partial results concerning the u-invariant of p-adic function fields are also shown. [ABSTRACT FROM AUTHOR]