On subset sums of a fixed set
Yong-Gao Chen (2003)
Acta Arithmetica
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Yong-Gao Chen (2003)
Acta Arithmetica
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James G. Huard, Kenneth S. Williams (2003)
Acta Arithmetica
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Jan Wójcik (1971)
Colloquium Mathematicae
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Valentin Blomer, Djordje Milićević (2015)
Journal of the European Mathematical Society
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We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
Mariusz Skałba (2012)
Acta Arithmetica
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Katalin Gyarmati, Imre Z. Ruzsa (2012)
Acta Arithmetica
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Jianya Liu, Tao Zhan (2001)
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. ...
Tsz Ho Chan (2006)
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.
Tomasz Schoen (2011)
Acta Arithmetica
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Jagy, William C., Kaplansky, Irving (1995)
Experimental Mathematics
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Kurt Girstmair, Johannes Schoißengeier (2005)
Acta Arithmetica
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J.H.E. Cohn (1983)
Mathematica Scandinavica
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J.H.E. Cohn (1983)
Mathematica Scandinavica
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R. de la Bretèche, T. D. Browning (2006)
Acta Arithmetica
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Christopher Hooley (1994)
Journal für die reine und angewandte Mathematik
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Heng Huat Chan, Shaun Cooper, Wen-Chin Liaw (2008)
Acta Arithmetica
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R. Baeza, D. Leep, M. O'Ryan (1986)
Mathematische Zeitschrift
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