An Asymptotic Estimate for Heights of Algebraic Subspaces

DOI10.2307/2154015zbMath0773.11041OpenAlexW4254355384MaRDI QIDQ3993861

Jeffrey Lin Thunder

Publication date: 13 August 1992

Full work available at URL: https://doi.org/10.2307/2154015

zbMATH Keywords

heightaffine spaceWeil heightbounded domainalgebraic number fieldestimate for number of lattice pointsexplicit asymptotic estimatenumber of linear subspaces

Mathematics Subject Classification ID

Arithmetic algebraic geometry (Diophantine geometry) (11G99) Nonconvex bodies (11H16) Diophantine approximation, transcendental number theory (11J99)

Related Items (9)

Counting subspaces of given height defined over a function field ⋮ Counting rational points of a Grassmannian ⋮ Deep hole lattices and isogenies of elliptic curves ⋮ The relative theorem of Schanuel ⋮ Unnamed Item ⋮ Counting points of fixed degree and bounded height on linear varieties ⋮ Siegel's Lemma with additional conditions ⋮ On the distribution of points in projective space of bounded height ⋮ Counting algebraic numbers with large height II

Cites Work

• Rational points of bounded height on Fano varieties
• The number of solutions of bounded height to a system of linear equations
• On heights of algebraic subspaces and diophantine approximations
• Asymptotic formulae for point lattices of bounded determinant and subspaces of bounded height
• An Introduction to the Geometry of Numbers
• Heights in number fields
• A theorem on transfer for convex bodies
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