Waring's problem for fields

William Ellison. "Waring's problem for fields." Acta Arithmetica 159.4 (2013): 315-330. <http://eudml.org/doc/279102>.

@article{WilliamEllison2013,
abstract = {If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of kth powers in certain function fields K(X).},
author = {William Ellison},
journal = {Acta Arithmetica},
keywords = {sums of squares; sums of higher powers; Pythagoras number; Waring's problem; formally real field; rational function field},
language = {eng},
number = {4},
pages = {315-330},
title = {Waring's problem for fields},
url = {http://eudml.org/doc/279102},
volume = {159},
year = {2013},
}

TY - JOUR
AU - William Ellison
TI - Waring's problem for fields
JO - Acta Arithmetica
PY - 2013
VL - 159
IS - 4
SP - 315
EP - 330
AB - If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of kth powers in certain function fields K(X).
LA - eng
KW - sums of squares; sums of higher powers; Pythagoras number; Waring's problem; formally real field; rational function field
UR - http://eudml.org/doc/279102
ER -