Forms in many variables
B. J. Birch
Source record
Source: Crossref
Published: Jan 23, 1962
DOI: 10.1098/rspa.1962.0007
Open original source ↗Source abstract
Abstract It is proved that if f is a homogeneous form of degree d with rational coefficients then the variety V:f = 0 certainly has rational points if it has non-singular real points and nonsingular p-adic points for every p, and if its singular locus has codimension sufficiently large compared with the degree d. The methods used are derived from those of Davenport (1959); considerable generalizations are made, and geometric conditions have to be introduced. The discussion of the singular integral presents unexpected difficulty.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.