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Waring's problem for fields

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Ellison W.

Acta Arithmetica

2013

tom 159

nr 4

315-330

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).

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1 Acta Arithmetica

1 Ellison W.

1 2013

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Waring's problem for fields