On Waring's problem (elementary methods).
Nesterenko, Yu.V. (2005)
Journal of Mathematical Sciences (New York)
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Nesterenko, Yu.V. (2005)
Journal of Mathematical Sciences (New York)
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M. Dodson, A. Tietäväinen (1976)
Acta Arithmetica
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K. Thanigasalam (1982)
Acta Arithmetica
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M. Z. Garaev (2003)
Acta Arithmetica
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Jagy, William C., Kaplansky, Irving (1995)
Experimental Mathematics
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Jörg Brüdern (2012)
Acta Arithmetica
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Koichi Kawada, Trevor D. Wooley (2002)
Acta Arithmetica
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Siu-lun Alan Lee (2012)
Acta Arithmetica
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Dirk Daemen (2010)
Acta Arithmetica
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James G. Huard, Kenneth S. Williams (2003)
Acta Arithmetica
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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.
Jan Wójcik (1971)
Colloquium Mathematicae
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Scott T. Parsell (2009)
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...
Trevor D. Wooley (1995)
Inventiones mathematicae
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Zhi-Wei Sun (2007)
Acta Arithmetica
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