English

Zeros of p-adic forms

Number Theory 2014-02-26 v2

Abstract

A variant of Brauer's induction method is developed. It is shown that quartic p-adic forms with at least 9127 variables have non-trivial zeros, for every p. For odd p considerably fewer variables are needed. There are also subsidiary new results concerning quintic forms, and systems of forms.

Keywords

Cite

@article{arxiv.0805.0534,
  title  = {Zeros of p-adic forms},
  author = {D. R. Heath-Brown},
  journal= {arXiv preprint arXiv:0805.0534},
  year   = {2014}
}

Comments

Misprints and other errors corrected, leading to a small improvement

R2 v1 2026-06-21T10:37:26.443Z