Images of Additive Polynomials in Fq ((t)) Have the Optimal Approximation Property
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 71-79
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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.
Dries, Lou van den; Kuhlmann, Franz-Viktor. Images of Additive Polynomials in Fq ((t)) Have the Optimal Approximation Property. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 71-79. doi: 10.4153/CMB-2002-007-5
@article{10_4153_CMB_2002_007_5,
author = {Dries, Lou van den and Kuhlmann, Franz-Viktor},
title = {Images of {Additive} {Polynomials} in {Fq} ((t)) {Have} the {Optimal} {Approximation} {Property}},
journal = {Canadian mathematical bulletin},
pages = {71--79},
year = {2002},
volume = {45},
number = {1},
doi = {10.4153/CMB-2002-007-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-007-5/}
}
TY - JOUR AU - Dries, Lou van den AU - Kuhlmann, Franz-Viktor TI - Images of Additive Polynomials in Fq ((t)) Have the Optimal Approximation Property JO - Canadian mathematical bulletin PY - 2002 SP - 71 EP - 79 VL - 45 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-007-5/ DO - 10.4153/CMB-2002-007-5 ID - 10_4153_CMB_2002_007_5 ER -
%0 Journal Article %A Dries, Lou van den %A Kuhlmann, Franz-Viktor %T Images of Additive Polynomials in Fq ((t)) Have the Optimal Approximation Property %J Canadian mathematical bulletin %D 2002 %P 71-79 %V 45 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-007-5/ %R 10.4153/CMB-2002-007-5 %F 10_4153_CMB_2002_007_5
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