Waring's problem for fields

• Autorzy: William Ellison
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 11P05: Waring's problem and variants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 159
• Numer: 4
• Strony: 315-330

Daty

wydano

2013

Twórcy

autor

William Ellison

• 15 allée de la Borde, 33450 St Sulpice et Cameyrac, France

Identyfikatory

DOI

10.4064/aa159-4-2