Integral points of small height outside of a hypersurface

DOI10.1007/s00605-005-0333-0zbMath1091.11024arXivmath/0409374OpenAlexW2152866614MaRDI QIDQ2494351

Lenny Fukshansky

Publication date: 26 June 2006

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409374

zbMATH Keywords

heightpolynomialslatticesSiegel's lemmalinear form

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Lattices and convex bodies (number-theoretic aspects) (11H06) Heights (11G50) Linear Diophantine equations (11D04) Products of linear forms (11H46)

Related Items (12)

On an effective variation of Kronecker’s approximation theorem avoiding algebraic sets ⋮ Non-reduced fibers of an arithmetic scheme ⋮ Counting basis extensions in a lattice ⋮ On sets of linear forms of maximal complexity ⋮ Helly numbers of algebraic subsets of \(\mathbb{R}^{d}\) and an extension of Doignon's theorem ⋮ Algebraic points of small height missing a union of varieties ⋮ Siegel's Lemma with additional conditions ⋮ Note on adelic triangulations and an adelic Blichfeldt-type inequality ⋮ Search bounds for zeros of polynomials over the algebraic closure of \(\mathbb Q\) ⋮ Adelic geometry of numbers and generalized Siegel lemmas ⋮ Positive semigroups in lattices and totally real number fields ⋮ On zeros of multilinear polynomials

Cites Work

• On Siegel's lemma
• Diophantine approximation on abelian varieties
• The number of solutions of bounded height to a system of linear equations
• Small zeros of quadratic forms with linear conditions
• A local Riemann hypothesis. I
• Siegel's Lemma with additional conditions
• An Introduction to the Geometry of Numbers
• Lipschitz² : A New Version of an Old Principle
• Covering lattice points by subspaces

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