Generalizations of Dedekind sums and their reciprocity laws
Yumiko Nagasaka, Kaori Ota, Chizuru Sekine (2003)
Acta Arithmetica
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Yumiko Nagasaka, Kaori Ota, Chizuru Sekine (2003)
Acta Arithmetica
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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].
Abdelmejid Bayad, Abdelaziz Raouj (2010)
Acta Arithmetica
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Wenpeng Zhang (2003)
Acta Arithmetica
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Zhi-Wei Sun (2001)
Acta Arithmetica
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Zhefeng Xu, Wenpeng Zhang (2008)
Acta Arithmetica
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Tingting Wang (2012)
Acta Arithmetica
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L. Carlitz (1964)
Mathematische Zeitschrift
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Vsevolod F. Lev (2008)
Acta Arithmetica
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L. Carlitz (1976)
Acta Arithmetica
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Kazuhito Kozuka (2011)
Acta Arithmetica
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Sun, Zhiwei (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Matthias Beck, Anastasia Chavez (2011)
Acta Arithmetica
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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.