Zeros of Systems of ${\mathfrak p}$-adic Quadratic Forms
Number Theory
2009-04-24 v2
Abstract
It is shown that a system of quadratic forms over a -adic field has a non-trivial common zero as soon as the number of variables exceeds , providing that the residue class field has cardinality at least .
Cite
@article{arxiv.0810.1122,
title = {Zeros of Systems of ${\mathfrak p}$-adic Quadratic Forms},
author = {D. R. Heath-Brown},
journal= {arXiv preprint arXiv:0810.1122},
year = {2009}
}
Comments
Revised version, with better treatment and results for characteristic 2