Sums of twelve squares
James G. Huard, Kenneth S. Williams (2003)
Acta Arithmetica
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James G. Huard, Kenneth S. Williams (2003)
Acta Arithmetica
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Jagy, William C., Kaplansky, Irving (1995)
Experimental Mathematics
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Ajai Choudhry, Jarosław Wróblewski (2012)
Acta Arithmetica
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Jan Wójcik (1971)
Colloquium Mathematicae
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Mariusz Skałba (2012)
Acta Arithmetica
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Noriko Hirata-Kohno, Shanta Laishram, T. N. Shorey, R. Tijdeman (2007)
Acta Arithmetica
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Zhi-Wei Sun (2007)
Acta Arithmetica
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Roger Clement Crocker (2008)
Colloquium Mathematicae
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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...
Alfred Moessner, George Xeroudakes (1954)
Publications de l'Institut Mathématique
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Todd Cochrane, Jeremy Coffelt, Christopher Pinner (2005)
Acta Arithmetica
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Géza Kós (2001)
Acta Arithmetica
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Jean Bourgain, Todd Cochrane, Jennifer Paulhus, Christopher Pinner (2011)
Acta Arithmetica
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Chang Leran, Li Xiaoxue (2016)
Open Mathematics
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In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
Gautami Bhowmik, Jan-Christoph Schlage-Puchta (2010)
Acta Arithmetica
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Anirban Mukhopadhyay, T. N. Shorey (2003)
Acta Arithmetica
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Florian Luca, P. G. Walsh (2001)
Acta Arithmetica
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Jörg Brüdern (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.
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...
Jianya Liu, Tao Zhan (2001)
Acta Arithmetica
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