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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

An asymptotic estimate for heights of algebraic subspaces


Author: Jeffrey Lin Thunder
Journal: Trans. Amer. Math. Soc. 331 (1992), 395-424
MSC: Primary 11G35; Secondary 11H16
DOI: https://doi.org/10.1090/S0002-9947-1992-1072102-0
MathSciNet review: 1072102
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Abstract: We count the number of subspaces of affine space with a given dimension defined over an algebraic number field with height less than or equal to $ B$. We give an explicit asymptotic estimate for the number of such subspaces as $ B$ goes to infinity, where the constants involved depend on the classical invariants of the number field (degree, discriminant, class number, etc.). The problem is reformulated as an estimate for the number of lattice points in a certain bounded domain.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1072102-0
Article copyright: © Copyright 1992 American Mathematical Society

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