Zeros of Systems of $\mathfrak{p}$-adic Quadratic Forms

Abstract

It is shown that a system of $r$ quadratic forms over a $\mathfrak{p}$-adic field has a non-trivial common zero as soon as the number of variables exceeds $4r$, providing that the residue class field has cardinality at least $(2r{)}^r$.

Revised version, with better treatment and results for characteristic 2