The density of rational lines on hypersurfaces: a bihomogeneous perspective
Artikel i vetenskaplig tidskrift, 2021

Let F be a non-singular homogeneous polynomial of degree d in n variables. We give an asymptotic formula of the pairs of integer points (x, y) with | x| ⩽ X and | y| ⩽ Y which generate a line lying in the hypersurface defined by F, provided that n> 2 d-1d4(d+ 1) (d+ 2). In particular, by restricting to Zariski-open subsets we are able to avoid imposing any conditions on the relative sizes of X and Y.

Forms in many variables

Hardy–Littlewood method

Rational lines

Författare

Julia Brandes

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Monatshefte für Mathematik

0026-9255 (ISSN) 1436-5081 (eISSN)

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Diskret matematik

DOI

10.1007/s00605-021-01528-6

Mer information

Senast uppdaterat

2021-03-24