On the number of linear spaces on hypersurfaces with a prescribed discriminant
Journal article, 2018

For a given form we apply the circle method in order to give an asymptotic estimate of the number of m-tuples spanning a linear space on the hypersurface with the property that . This allows us in some measure to count rational linear spaces on hypersurfaces whose underlying integer lattice is primitive.

Forms in many variables

Linear spaces


Julia Brandes

University of Waterloo

Chalmers, Mathematical Sciences, Algebra and geometry

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 289 3-4 803-827

Subject Categories


Probability Theory and Statistics

Mathematical Analysis



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