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

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

2008-10-07

arxiv.org/abs/0810.1122v2

Mathematics

Number Theory

Revised version, with better treatment and results for characteristic 2

Scientific paper

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 $(2r)^r$.

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