Universal Waring theorems with cubic summands
L. Dickson (1936)
Prace Matematyczno-Fizyczne
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L. Dickson (1936)
Prace Matematyczno-Fizyczne
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Alfred Moessner, George Xeroudakes (1954)
Publications de l'Institut Mathématique
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Vsevolod F. Lev (2008)
Acta Arithmetica
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Koichi Kawada, Trevor D. Wooley (2002)
Acta Arithmetica
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Zhi-Wei Sun (2001)
Acta Arithmetica
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Jagy, William C., Kaplansky, Irving (1995)
Experimental Mathematics
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Trevor D. Wooley (2015)
Acta Arithmetica
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Estimates are provided for sth moments of cubic smooth Weyl sums, when 4 ≤ s ≤ 8, by enhancing the author's iterative method that delivers estimates beyond classical convexity. As a consequence, an improved lower bound is presented for the number of integers not exceeding X that are represented as the sum of three cubes of natural numbers.
Tingting Wang (2012)
Acta Arithmetica
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Imre Z. Ruzsa (2004)
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...
Kuba, Markus, Prodinger, Helmut, Schneider, Carsten (2008)
Integers
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Sun, Zhiwei (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Huaning Liu, Wenpeng Zhang (2007)
Acta Arithmetica
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