Artin's Conjecture on Zeros of p-Adic Forms

2010/02/19 by D. R. Heath‐Brown, D. R. Heath-Brown, Heath-Brown, D. R.
Mathematics · #11D88 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D88

paper · pdf · doi:10.48550/arxiv.1002.3754

Submitted for publication as part of ICM 2010

arxiv created 2010/02/19 · openalex publication_date 2010/02/19 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an exposition of work on Artin's Conjecture on the zeros of p-adic forms. A variety of lines of attack are described, going back to 1945. However there is particular emphasis on recent developments concerning quartic forms on the one hand, and systems of quadratic forms on the other.

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