Displaying similar documents to “A geometric proof of Kummer's reciprocity law for seventh powers”

The hybrid power mean of quartic Gauss sums and Kloosterman sums

Li Xiaoxue, Hu Jiayuan (2017)

Open Mathematics

Similarity:

The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.

Equality of Dedekind sums modulo 8ℤ

Emmanuel Tsukerman (2015)

Acta Arithmetica

Similarity:

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].