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Displaying similar documents to “The binary Goldbach problem with arithmetic weights attached to one of the variables”

Kloosterman sums in residue classes

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.

On the sum of two squares and two powers of k

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. ...

Sums of Squares Coprime in Pairs

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.