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On the number of linear spaces on hypersurfaces with a prescribed discriminant

Journal article
Authors Julia Brandes
Published in Mathematische Zeitschrift
Volume 289
Issue 3-4
Pages 803-827
ISSN 0025-5874
Publication year 2018
Published at Department of Mathematical Sciences, Algebra and Geometry
Pages 803-827
Language en
Links https://doi.org/10.1007/s00209-017-...
Keywords Forms in many variables, Linear spaces
Subject categories Mathematics

Abstract

© 2017 The Author(s) For a given form (Formula presented.) we apply the circle method in order to give an asymptotic estimate of the number of m-tuples (Formula presented.) spanning a linear space on the hypersurface (Formula presented.) with the property that (Formula presented.). This allows us in some measure to count rational linear spaces on hypersurfaces whose underlying integer lattice is primitive.

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