Images of additive polynomials in double-struck F signq((t)) have the optimal approximation property

Lou Van den Dries; Franz Viktor Kuhlmann

doi:10.4153/CMB-2002-007-5

Images of additive polynomials in double-struck F sign_q((t)) have the optimal approximation property

Lou Van den Dries, Franz Viktor Kuhlmann

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

Abstract

We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property: every element in the field has a (not necessarily unique) closest approximation in this set of values. The approximation is with respect to the canonical valuation on the field. This property is elementary in the language of valued rings.

Original language	English (US)
Pages (from-to)	71-79
Number of pages	9
Journal	Canadian Mathematical Bulletin
Volume	45
Issue number	1
DOIs	https://doi.org/10.4153/CMB-2002-007-5
State	Published - Mar 2002

ASJC Scopus subject areas

Mathematics(all)

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Cite this

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abstract = "We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property: every element in the field has a (not necessarily unique) closest approximation in this set of values. The approximation is with respect to the canonical valuation on the field. This property is elementary in the language of valued rings.",

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