Zeros of <i>p</i> -adic forms

D. R. Heath‐Brown

Type: Article

Publication Date: 2009-11-12

Citations: 18

DOI: https://doi.org/10.1112/plms/pdp043

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.

Locations

Proceedings of the London Mathematical Society - View
arXiv (Cornell University) - View - PDF
DataCite API - View

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+ PDF Chat	On a Local-Global Principle for H 3 of Function Fields of Surfaces over a Finite Field	2017	Alena Pirutka
+	Zeros of p-adic forms	2009	Jahan Zahid
+ PDF Chat	u-Invariants for forms of higher degree	2008	S. Pumplün
+ PDF Chat	Improvements in Birch’s theorem on forms in many variables	2015	T. D. Browning Sean Prendiville
+	Quartic Forms in Many Variables	2014	Jan H. Dumke
+ PDF Chat	Artin's Conjecture on Zeros of p-adic Forms	2011	D. R. Heath‐Brown
+	Improvements in Birch's theorem on forms in many variables	2014	T. D. Browning Sean Prendiville
+	Cubic diophantine inequalities for split forms	2013	Sam Chow

Works Cited by This (12)

Action	Title	Year	Authors
+ PDF Chat	On systems of three quadratic forms	1980	Susan Schuur
+	Quintic Forms overp-adic Fields	1996	David B. Leep Charles C. Yeomans
+	Linear Spaces on the Intersection of Two Quadratic Hypersurfaces, and Systems of p-adic Quadratic Forms	2005	Rainer Dietmann
+	The u-invariant of p-adic function fields	2012	David B. Leep
+ PDF Chat	Solubility of Systems of Quadratic Forms	1997	Greg Martin
+	The number of points on a singular curve over a finite field	1994	David B. Leep Charles C. Yeomans
+	Bounds on transfer principles for algebraically closed and complete discretely valued fields	1978	Scott Shorey Brown
+	Homogeneous additive equations	1963	H. Davenport D. J. Lewis
+	Diophantine Problems Over Local Fields II. A Complete Set of Axioms for p-Adic Number Theory	1965	James Ax Simon Kochen
+	Systems of quadratic forms.	1984	David B. Leep