Higher dimensional Dedekind sums in function fields
Abdelmejid Bayad, Yoshinori Hamahata (2012)
Acta Arithmetica
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Abdelmejid Bayad, Yoshinori Hamahata (2012)
Acta Arithmetica
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William Ellison (2013)
Acta Arithmetica
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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...
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Electronic Research Announcements of the American Mathematical Society [electronic only]
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