Counting primitive points of bounded height

DOI10.1090/S0002-9947-10-05173-1zbMath1270.11064arXiv1204.0927OpenAlexW3103655229MaRDI QIDQ4930021

Martin Widmer

Publication date: 27 September 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0927

zbMATH Keywords

Weil heightLipschitz parametrizationAdelic Lipschitz heightSchmidt partition

Mathematics Subject Classification ID

Varieties over global fields (11G35) Heights (11G50) Diophantine inequalities (11D75)

Related Items (21)

Computing points of bounded height in projective space over a number field ⋮ WEAK ADMISSIBILITY, PRIMITIVITY, O‐MINIMALITY, AND DIOPHANTINE APPROXIMATION ⋮ Asymptotic Diophantine approximation: the multiplicative case ⋮ Averages and higher moments for the \(\ell\)-torsion in class groups ⋮ Orbits of Algebraic Dynamical Systems in Subgroups and Subfields ⋮ On the number of reducible polynomials of bounded naive height ⋮ The Schanuel theorem in adelic Hermitian bundles ⋮ Counting rational points of a Grassmannian ⋮ Explicit counting of ideals and a Brun–Titchmarsh inequality for the Chebotarev density theorem ⋮ On the number of integer points in a multidimensional domain ⋮ ON NUMBER FIELDS WITH NONTRIVIAL SUBFIELDS ⋮ Joint distribution of conjugate algebraic numbers: a random polynomial approach ⋮ Counting points of fixed degree and bounded height on linear varieties ⋮ Joint distribution of spins ⋮ Siegel's lemma is sharp for almost all linear systems ⋮ Spins of prime ideals and the negative Pell equation ⋮ Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions ⋮ Lipschitz class, narrow class, and counting lattice points ⋮ On the distribution of Salem numbers ⋮ Counting ideals in ray classes ⋮ Uniform bounds for lattice point counting and partial sums of zeta functions

Cites Work

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• Northcott's theorem on heights II. The quadratic case
• Counting algebraic numbers with large height II
• Counting Algebraic Numbers with Large Height I
• Counting points of fixed degree and bounded height
• On the zeros of the derivative of a polynomial
• Heights in number fields

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