### Limit reduced powers

A. Wojciechowska (1969)

Colloquium Mathematicae

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A. Wojciechowska (1969)

Colloquium Mathematicae

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Alfred Moessner, George Xeroudakes (1954)

Publications de l'Institut Mathématique

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Koichi Kawada, Trevor D. Wooley (2002)

Acta Arithmetica

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Jörg Brüdern (2012)

Acta Arithmetica

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Jagy, William C., Kaplansky, Irving (1995)

Experimental Mathematics

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Vsevolod F. Lev (2008)

Acta Arithmetica

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Lajos Hajdu, Shanta Laishram, Szabolcs Tengely (2016)

Acta Arithmetica

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We investigate power values of sums of products of consecutive integers. We give general finiteness results, and also give all solutions when the number of terms in the sum considered is at most ten.

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...

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.

R.C. Vaughan (1986)

Journal für die reine und angewandte Mathematik

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L. Dickson (1936)

Prace Matematyczno-Fizyczne

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Liqun Hu, Li Yang (2011)

Acta Arithmetica

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