Grids with dense values

Uri Shapira

doi:10.4171/CMH/293

Grids with dense values

Uri Shapira

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Given a continuous function from Euclidean space to the real line, we analyze (under some natural assumption on the function), the set of values it takes on translates of lattices. Our results are of the flavor: For almost any translate the set of values is dense in the set of possible values. The results are then applied to a variety of concrete examples obtaining new information in classical discussions in different areas in mathematics; in particular, Minkowski's conjecture regarding products of inhomogeneous forms and inhomogeneous Diophantine approximations.

Original language	English
Pages (from-to)	485-506
Number of pages	22
Journal	Commentarii Mathematici Helvetici
Volume	88
Issue number	2
DOIs	https://doi.org/10.4171/CMH/293
State	Published - 2013

Keywords

Diophantine approximation
Grids
Lattices
Minkowski's conjecture
Non-singular forms

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4171/CMH/293

Cite this

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KW - Non-singular forms

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Grids with dense values

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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