English

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

Number Theory 2009-04-24 v2

Abstract

It is shown that a system of rr quadratic forms over a p{\mathfrak p}-adic field has a non-trivial common zero as soon as the number of variables exceeds 4r4r, providing that the residue class field has cardinality at least (2r)r(2r)^r.

Keywords

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

R2 v1 2026-06-21T11:28:01.151Z