Subset sums avoiding quadratic nonresidues

Péter Csikvári

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Displaying similar documents to “Subset sums avoiding quadratic nonresidues”

On subset sums of a fixed set

Yong-Gao Chen (2003)

Acta Arithmetica

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Zones of large and small values for Dedekind sums

Kurt Girstmair (2003)

Acta Arithmetica

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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 arithmetic mean of Dedekind sums

Kurt Girstmair, Johannes Schoißengeier (2005)

Acta Arithmetica

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Note on a product formula for the Bayad function and a law of quadratic reciprocity

Heima Hayashi (2011)

Acta Arithmetica

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Note on the quadratic Gauss sums.

Danas, George (2001)

International Journal of Mathematics and Mathematical Sciences

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Dedekind sums with characters and class numbers of imaginary quadratic fields

Kaori Ota (2003)

Acta Arithmetica

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Bounds for quadratic Waring's problem

Myung-Hwan Kim, Byeong-Kweon Oh (2002)

Acta Arithmetica

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Equality of Dedekind sums modulo 8ℤ

Emmanuel Tsukerman (2015)

Acta Arithmetica

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Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].