### Infinite sums as linear combinations of polygamma functions

Kh. Hessami Pilehrood, T. Hessami Pilehrood (2007)

Acta Arithmetica

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Kh. Hessami Pilehrood, T. Hessami Pilehrood (2007)

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Zhi-Wei Sun (2001)

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Chester Weatherby (2010)

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Zhefeng Xu, Wenpeng Zhang (2008)

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Vsevolod F. Lev (2008)

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Tingting Wang (2012)

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L. Carlitz (1980)

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Yumiko Nagasaka, Kaori Ota, Chizuru Sekine (2003)

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Alfred Moessner, George Xeroudakes (1954)

Publications de l'Institut Mathématique

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Li Xiaoxue, Hu Jiayuan (2017)

Open Mathematics

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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.

Sun, Zhiwei (2003)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Huaning Liu, Wenpeng Zhang (2007)

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Wenpeng Zhang (2003)

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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.

Wenpeng Zhang, Zhaoxia Wu (2010)

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Emmanuel Tsukerman (2015)

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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].