Zeros of Systems of \mathfrak p-adic Quadratic Forms

2008/10/07 by D. R. Heath‐Brown, D. R. Heath-Brown, Heath-Brown, D. R.
Mathematics · #11D88 #11E08 #11E95 #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11D88 #msc:11E08 #msc:11E95

paper · pdf · doi:10.48550/arxiv.0810.1122

Revised version, with better treatment and results for characteristic 2

openalex publication_date 2008/10/07 · arxiv created 2009/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Diophantine Problems Over Local Fields I

Related

• p-adic Zeros of Quintic Forms
• Quartic Forms in Many Variables
• Artin's Conjecture on Zeros of p-Adic Forms
• Solubility of Systems of Quadratic Forms
• Relationships between p-unit constructions for real quadratic fields